Images | Archived scripts and data files
This page contains images, code files (scripts), and data files used in the notes, publications, and underlying research for the tilings project. Many of the files, especially code and data files are stored in a Google Drive folder constructed especially for this site.
Images
Most of the images may be directly viewed on this tilings site. All of the images are stored are in this Google Drive images folder.
Surfaces and tiled surfaces
Images in the table below are stored in this Google Drive images folder
| genus two surface | genus2.gif | genus2.eps |
| icosahedral tiling of sphere | icos.gif | icos.eps |
| (2,4,4) tiling on a torus | torus244.gif | torus244.eps |
| (3,3,3) tiling on a torus | torus333.gif | torus333.eps |
Hyperbolic tilings
Images in the table below are stored in this Google Drive images folder
Divisible tilings
A tiling is divisible if it can be divided into a finer kaleidoscopic tiling. An example is the tiling of the torus by rectangles which is refined by the tiling by (2,4,4) triangles, pictured below. Each divisible tiling of a surface comes from a divisible tiling of the hyperbolic plane. All such tilings have been classified . There are four types of tilings. The description and links to the tables and pictures are below:
- Eight cases of tilings of triangles. There are six infinite families and two exceptional cases.
- Thirty four cases tilings of quadrilaterals by triangles with free vertices. Because there are free vertices each one gives rise to infinite family of divisible tilings.
- Twenty seven tilings of quadrilaterals by triangles without free
vertices.
There are no families. - Two tilings of quadrilaterals by quadrilaterals.
Archived scripts and data files
This section contains links to various code files (scripts, as I call them) and data files used to investigate tilings on surfaces. The archives, located in this Google Drive scripts an data folder, are organized by the background notes and the various project areas as in the jump table below. The more important files will have direct links, other links will simply take you to the appropriate folder. In the jump table the interpretation of various extensions is explained; only .mws, .m and .mat are standard. All files except Matlab data files, are simple text files. A library script or function library file is a package of related functions readable by the appropriate
application, say Maple or Magma.
| Jump and Information Table | ||||||||||||||||||||||||||||||||||||
| Background Notes | Research Project Areas | File Extension Interpretation | image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | Background Notes | Research Project Areas | File Extension Interpretation | image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | Background Notes | Research Project Areas | File Extension Interpretation | image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | Background Notes | Research Project Areas | File Extension Interpretation | image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | Background Notes | Research Project Areas | File Extension Interpretation | image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | ||||||
| Background Notes | Research Project Areas | File Extension Interpretation | ||||||||||||||||||||||||||||||||||
| image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | ||||||||||||||||||||||||||||||||||
| Background Notes | Research Project Areas | File Extension Interpretation | ||||||||||||||||||||||||||||||||||
| image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | ||||||||||||||||||||||||||||||||||
| Background Notes | Research Project Areas | File Extension Interpretation | ||||||||||||||||||||||||||||||||||
| image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | ||||||||||||||||||||||||||||||||||
| Background Notes | Research Project Areas | File Extension Interpretation | ||||||||||||||||||||||||||||||||||
| image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script | ||||||||||||||||||||||||||||||||||
| Background Notes | Research Project Areas | File Extension Interpretation | ||||||||||||||||||||||||||||||||||
| image scripts
| low genus classification – triangles – quadrilaterals divisible tilings geodesics, length spectrum and billiards moduli ovals separability of symmetries separability of symmetries – graphs tiler (create tilings with Matlab) | .mws Maple worksheet, .mpl Maple scripts and Maple library scripts .m Matlab script .mat Matlab data file
.mgm Magma scripts and library scripts .act .bdat .dat .rez various data .log transcript file .eps encapsulated post script |
Background Notes – Scripts
Producing Images
| Image drawing scripts – folder | ||||||||||||||||||||||||||||||||||||||||||||||||||
| icos.mws | icosahedral tiling of the sphere | torus244.mws | (2,4,4) tiling on the torus | torus333.mws | (3,3,3) tiling on the torus | genus2.mws | surface of genus two | triang4.mws | master tile (needs gtools.mpl) | icos.mws | icosahedral tiling of the sphere | torus244.mws | (2,4,4) tiling on the torus | torus333.mws | (3,3,3) tiling on the torus | genus2.mws | surface of genus two | triang4.mws | master tile (needs gtools.mpl) | icos.mws | icosahedral tiling of the sphere | torus244.mws | (2,4,4) tiling on the torus | torus333.mws | (3,3,3) tiling on the torus | genus2.mws | surface of genus two | triang4.mws | master tile (needs gtools.mpl) | icos.mws | icosahedral tiling of the sphere | torus244.mws | (2,4,4) tiling on the torus | torus333.mws | (3,3,3) tiling on the torus | genus2.mws | surface of genus two | triang4.mws | master tile (needs gtools.mpl) | ||||||||||
| icos.mws | icosahedral tiling of the sphere | |||||||||||||||||||||||||||||||||||||||||||||||||
| torus244.mws | (2,4,4) tiling on the torus | |||||||||||||||||||||||||||||||||||||||||||||||||
| torus333.mws | (3,3,3) tiling on the torus | |||||||||||||||||||||||||||||||||||||||||||||||||
| genus2.mws | surface of genus two | |||||||||||||||||||||||||||||||||||||||||||||||||
| triang4.mws | master tile (needs gtools.mpl) | |||||||||||||||||||||||||||||||||||||||||||||||||
| icos.mws | icosahedral tiling of the sphere | |||||||||||||||||||||||||||||||||||||||||||||||||
| torus244.mws | (2,4,4) tiling on the torus | |||||||||||||||||||||||||||||||||||||||||||||||||
| torus333.mws | (3,3,3) tiling on the torus | |||||||||||||||||||||||||||||||||||||||||||||||||
| genus2.mws | surface of genus two | |||||||||||||||||||||||||||||||||||||||||||||||||
| triang4.mws | master tile (needs gtools.mpl) | |||||||||||||||||||||||||||||||||||||||||||||||||
| icos.mws | icosahedral tiling of the sphere | |||||||||||||||||||||||||||||||||||||||||||||||||
| torus244.mws | (2,4,4) tiling on the torus | |||||||||||||||||||||||||||||||||||||||||||||||||
| torus333.mws | (3,3,3) tiling on the torus | |||||||||||||||||||||||||||||||||||||||||||||||||
| genus2.mws | surface of genus two | |||||||||||||||||||||||||||||||||||||||||||||||||
| triang4.mws | master tile (needs gtools.mpl) | |||||||||||||||||||||||||||||||||||||||||||||||||
| icos.mws | icosahedral tiling of the sphere | |||||||||||||||||||||||||||||||||||||||||||||||||
| torus244.mws | (2,4,4) tiling on the torus | |||||||||||||||||||||||||||||||||||||||||||||||||
| torus333.mws | (3,3,3) tiling on the torus | |||||||||||||||||||||||||||||||||||||||||||||||||
| genus2.mws | surface of genus two | |||||||||||||||||||||||||||||||||||||||||||||||||
| triang4.mws | master tile (needs gtools.mpl) |
Various Constructions and
Derivations
| Other scripts for notes – folder | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Hgeom.mws | Geometric constructions | DHgeom.mws | Invariance and distance calculations for the disc | UHgeom.mws | Invariance and distance calculations for the upper half plane | NSchwartz.mws | Numerical calculations for Schwartz triangles | schwartz.mws | Symbolic Calculations for Schwartz triangles | Hgeom.mws | Geometric constructions | DHgeom.mws | Invariance and distance calculations for the disc | UHgeom.mws | Invariance and distance calculations for the upper half plane | NSchwartz.mws | Numerical calculations for Schwartz triangles | schwartz.mws | Symbolic Calculations for Schwartz triangles | Hgeom.mws | Geometric constructions | DHgeom.mws | Invariance and distance calculations for the disc | UHgeom.mws | Invariance and distance calculations for the upper half plane | NSchwartz.mws | Numerical calculations for Schwartz triangles | schwartz.mws | Symbolic Calculations for Schwartz triangles | Hgeom.mws | Geometric constructions | DHgeom.mws | Invariance and distance calculations for the disc | UHgeom.mws | Invariance and distance calculations for the upper half plane | NSchwartz.mws | Numerical calculations for Schwartz triangles | schwartz.mws | Symbolic Calculations for Schwartz triangles | ||||||||||
| Hgeom.mws | Geometric constructions | |||||||||||||||||||||||||||||||||||||||||||||||||
| DHgeom.mws | Invariance and distance calculations for the disc | |||||||||||||||||||||||||||||||||||||||||||||||||
| UHgeom.mws | Invariance and distance calculations for the upper half plane | |||||||||||||||||||||||||||||||||||||||||||||||||
| NSchwartz.mws | Numerical calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||||||||||||
| schwartz.mws | Symbolic Calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||||||||||||
| Hgeom.mws | Geometric constructions | |||||||||||||||||||||||||||||||||||||||||||||||||
| DHgeom.mws | Invariance and distance calculations for the disc | |||||||||||||||||||||||||||||||||||||||||||||||||
| UHgeom.mws | Invariance and distance calculations for the upper half plane | |||||||||||||||||||||||||||||||||||||||||||||||||
| NSchwartz.mws | Numerical calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||||||||||||
| schwartz.mws | Symbolic Calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||||||||||||
| Hgeom.mws | Geometric constructions | |||||||||||||||||||||||||||||||||||||||||||||||||
| DHgeom.mws | Invariance and distance calculations for the disc | |||||||||||||||||||||||||||||||||||||||||||||||||
| UHgeom.mws | Invariance and distance calculations for the upper half plane | |||||||||||||||||||||||||||||||||||||||||||||||||
| NSchwartz.mws | Numerical calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||||||||||||
| schwartz.mws | Symbolic Calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||||||||||||
| Hgeom.mws | Geometric constructions | |||||||||||||||||||||||||||||||||||||||||||||||||
| DHgeom.mws | Invariance and distance calculations for the disc | |||||||||||||||||||||||||||||||||||||||||||||||||
| UHgeom.mws | Invariance and distance calculations for the upper half plane | |||||||||||||||||||||||||||||||||||||||||||||||||
| NSchwartz.mws | Numerical calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||||||||||||
| schwartz.mws | Symbolic Calculations for Schwartz triangles |
Project Scripts and Data
Low genus classification of tilings
and branching data for tilings
Triangle tilings
| Data Folder (also contains some branching data files) | ||||||||||
| abelian2.act
| two generator abelian rotation group actions
cyclic group rotation group actions non-solvable rotation group actions non-abelian p-group rotation group actions non-abelian non-p-group solvable rotation group | abelian2.act
| two generator abelian rotation group actions
cyclic group rotation group actions non-solvable rotation group actions non-abelian p-group rotation group actions non-abelian non-p-group solvable rotation group | abelian2.act
| two generator abelian rotation group actions
cyclic group rotation group actions non-solvable rotation group actions non-abelian p-group rotation group actions non-abelian non-p-group solvable rotation group | abelian2.act
| two generator abelian rotation group actions
cyclic group rotation group actions non-solvable rotation group actions non-abelian p-group rotation group actions non-abelian non-p-group solvable rotation group | ||
| abelian2.act
| two generator abelian rotation group actions
cyclic group rotation group actions non-solvable rotation group actions non-abelian p-group rotation group actions non-abelian non-p-group solvable rotation group | |||||||||
| abelian2.act
| two generator abelian rotation group actions
cyclic group rotation group actions non-solvable rotation group actions non-abelian p-group rotation group actions non-abelian non-p-group solvable rotation group | |||||||||
| abelian2.act
| two generator abelian rotation group actions
cyclic group rotation group actions non-solvable rotation group actions non-abelian p-group rotation group actions non-abelian non-p-group solvable rotation group | |||||||||
| abelian2.act
| two generator abelian rotation group actions
cyclic group rotation group actions non-solvable rotation group actions non-abelian p-group rotation group actions non-abelian non-p-group solvable rotation group |
| Scripts Folder (also contains some branching data input files) | ||||||||||||||||||||||||||||||
| A5.mgm | sample script to find (2,3,5) – tilings of the sphere with G = Alt(5), | tileclass.mgm | function library for computing tilings and calculating “theta” | tilerun.mgm
| master driver for tiling classification program find two generator abelian rotation groups find cyclic groups rotation groups find non-solvable rotation groups (permutation group format) find non-abelian p-group rotation groups (PC format) find non-abelian non-p-group solvable rotation groups (PC format) | A5.mgm | sample script to find (2,3,5) – tilings of the sphere with G = Alt(5), | tileclass.mgm | function library for computing tilings and calculating “theta” | tilerun.mgm
| master driver for tiling classification program find two generator abelian rotation groups find cyclic groups rotation groups find non-solvable rotation groups (permutation group format) find non-abelian p-group rotation groups (PC format) find non-abelian non-p-group solvable rotation groups (PC format) | A5.mgm | sample script to find (2,3,5) – tilings of the sphere with G = Alt(5), | tileclass.mgm | function library for computing tilings and calculating “theta” | tilerun.mgm
| master driver for tiling classification program find two generator abelian rotation groups find cyclic groups rotation groups find non-solvable rotation groups (permutation group format) find non-abelian p-group rotation groups (PC format) find non-abelian non-p-group solvable rotation groups (PC format) | A5.mgm | sample script to find (2,3,5) – tilings of the sphere with G = Alt(5), | tileclass.mgm | function library for computing tilings and calculating “theta” | tilerun.mgm
| master driver for tiling classification program find two generator abelian rotation groups find cyclic groups rotation groups find non-solvable rotation groups (permutation group format) find non-abelian p-group rotation groups (PC format) find non-abelian non-p-group solvable rotation groups (PC format) | ||||||
| A5.mgm | sample script to find (2,3,5) – tilings of the sphere with G = Alt(5), | |||||||||||||||||||||||||||||
| tileclass.mgm | function library for computing tilings and calculating “theta” | |||||||||||||||||||||||||||||
| tilerun.mgm
| master driver for tiling classification program find two generator abelian rotation groups find cyclic groups rotation groups find non-solvable rotation groups (permutation group format) find non-abelian p-group rotation groups (PC format) find non-abelian non-p-group solvable rotation groups (PC format) | |||||||||||||||||||||||||||||
| A5.mgm | sample script to find (2,3,5) – tilings of the sphere with G = Alt(5), | |||||||||||||||||||||||||||||
| tileclass.mgm | function library for computing tilings and calculating “theta” | |||||||||||||||||||||||||||||
| tilerun.mgm
| master driver for tiling classification program find two generator abelian rotation groups find cyclic groups rotation groups find non-solvable rotation groups (permutation group format) find non-abelian p-group rotation groups (PC format) find non-abelian non-p-group solvable rotation groups (PC format) | |||||||||||||||||||||||||||||
| A5.mgm | sample script to find (2,3,5) – tilings of the sphere with G = Alt(5), | |||||||||||||||||||||||||||||
| tileclass.mgm | function library for computing tilings and calculating “theta” | |||||||||||||||||||||||||||||
| tilerun.mgm
| master driver for tiling classification program find two generator abelian rotation groups find cyclic groups rotation groups find non-solvable rotation groups (permutation group format) find non-abelian p-group rotation groups (PC format) find non-abelian non-p-group solvable rotation groups (PC format) | |||||||||||||||||||||||||||||
| A5.mgm | sample script to find (2,3,5) – tilings of the sphere with G = Alt(5), | |||||||||||||||||||||||||||||
| tileclass.mgm | function library for computing tilings and calculating “theta” | |||||||||||||||||||||||||||||
| tilerun.mgm
| master driver for tiling classification program find two generator abelian rotation groups find cyclic groups rotation groups find non-solvable rotation groups (permutation group format) find non-abelian p-group rotation groups (PC format) find non-abelian non-p-group solvable rotation groups (PC format) |
Quadrilaterals
Tilings
|
Data
Folder Files are the form quads.vectors where s is the genus. Each entry contains branching data, group presentation, generating vectors and tiling status of the (k,l,m,n), ( k,m,l,n), and (k,l,n,m) twist of a generating vector . | ||||||||||||||||||||
|
Scripts
Folder (also contains some branching data input files) | ||||||||||||||||||||
| quadclass.mgm | function library for computing tilings and calculating “theta” | quadrun.mgm | master driver for tiling classification program | quadclass.mgm | function library for computing tilings and calculating “theta” | quadrun.mgm | master driver for tiling classification program | quadclass.mgm | function library for computing tilings and calculating “theta” | quadrun.mgm | master driver for tiling classification program | quadclass.mgm | function library for computing tilings and calculating “theta” | quadrun.mgm | master driver for tiling classification program | ||||
| quadclass.mgm | function library for computing tilings and calculating “theta” | |||||||||||||||||||
| quadrun.mgm | master driver for tiling classification program | |||||||||||||||||||
| quadclass.mgm | function library for computing tilings and calculating “theta” | |||||||||||||||||||
| quadrun.mgm | master driver for tiling classification program | |||||||||||||||||||
| quadclass.mgm | function library for computing tilings and calculating “theta” | |||||||||||||||||||
| quadrun.mgm | master driver for tiling classification program | |||||||||||||||||||
| quadclass.mgm | function library for computing tilings and calculating “theta” | |||||||||||||||||||
| quadrun.mgm | master driver for tiling classification program |
Branching data
| Data and Script Folder | ||||||||||
| bradatpoly.mws | branching data for small polygons and low genus | bradatpoly.mws | branching data for small polygons and low genus | bradatpoly.mws | branching data for small polygons and low genus | bradatpoly.mws | branching data for small polygons and low genus | ||
| bradatpoly.mws | branching data for small polygons and low genus | |||||||||
| bradatpoly.mws | branching data for small polygons and low genus | |||||||||
| bradatpoly.mws | branching data for small polygons and low genus | |||||||||
| bradatpoly.mws | branching data for small polygons and low genus |
Divisible Tilings
The final images for the divisible tilings were constructed from the
intermediate
result files listed here and the Matlab tiling scripts, also listed
here.
| Data and Images Folders | ||||||||||||||||||||||||||||||
| Boundary Construction | .rez and .log files containing information on all divisible quadrilaterals constructible by boundary construction method | Direct Construction | .mpl files containing information on all divisible quadrilaterals constructible by direct construction method | Images | folder containing divisible quadrilaterals constructible by direct construction methods as .mpl files | Boundary Construction | .rez and .log files containing information on all divisible quadrilaterals constructible by boundary construction method | Direct Construction | .mpl files containing information on all divisible quadrilaterals constructible by direct construction method | Images | folder containing divisible quadrilaterals constructible by direct construction methods as .mpl files | Boundary Construction | .rez and .log files containing information on all divisible quadrilaterals constructible by boundary construction method | Direct Construction | .mpl files containing information on all divisible quadrilaterals constructible by direct construction method | Images | folder containing divisible quadrilaterals constructible by direct construction methods as .mpl files | Boundary Construction | .rez and .log files containing information on all divisible quadrilaterals constructible by boundary construction method | Direct Construction | .mpl files containing information on all divisible quadrilaterals constructible by direct construction method | Images | folder containing divisible quadrilaterals constructible by direct construction methods as .mpl files | ||||||
| Boundary Construction | .rez and .log files containing information on all divisible quadrilaterals constructible by boundary construction method | |||||||||||||||||||||||||||||
| Direct Construction | .mpl files containing information on all divisible quadrilaterals constructible by direct construction method | |||||||||||||||||||||||||||||
| Images | folder containing divisible quadrilaterals constructible by direct construction methods as .mpl files | |||||||||||||||||||||||||||||
| Boundary Construction | .rez and .log files containing information on all divisible quadrilaterals constructible by boundary construction method | |||||||||||||||||||||||||||||
| Direct Construction | .mpl files containing information on all divisible quadrilaterals constructible by direct construction method | |||||||||||||||||||||||||||||
| Images | folder containing divisible quadrilaterals constructible by direct construction methods as .mpl files | |||||||||||||||||||||||||||||
| Boundary Construction | .rez and .log files containing information on all divisible quadrilaterals constructible by boundary construction method | |||||||||||||||||||||||||||||
| Direct Construction | .mpl files containing information on all divisible quadrilaterals constructible by direct construction method | |||||||||||||||||||||||||||||
| Images | folder containing divisible quadrilaterals constructible by direct construction methods as .mpl files | |||||||||||||||||||||||||||||
| Boundary Construction | .rez and .log files containing information on all divisible quadrilaterals constructible by boundary construction method | |||||||||||||||||||||||||||||
| Direct Construction | .mpl files containing information on all divisible quadrilaterals constructible by direct construction method | |||||||||||||||||||||||||||||
| Images | folder containing divisible quadrilaterals constructible by direct construction methods as .mpl files |
| Scripts Folder | ||||||||||||||||||||||||||||||
| tiling m-file folder | folder of Matlab scripts to that draw tilings by triangles | Boundary Construction | folder of Maple scripts to determine divisible quadrilaterals by boundary construction method (also contains log and rez files) | Direct Construction | folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as | tiling m-file folder | folder of Matlab scripts to that draw tilings by triangles | Boundary Construction | folder of Maple scripts to determine divisible quadrilaterals by boundary construction method (also contains log and rez files) | Direct Construction | folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as | tiling m-file folder | folder of Matlab scripts to that draw tilings by triangles | Boundary Construction | folder of Maple scripts to determine divisible quadrilaterals by boundary construction method (also contains log and rez files) | Direct Construction | folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as | tiling m-file folder | folder of Matlab scripts to that draw tilings by triangles | Boundary Construction | folder of Maple scripts to determine divisible quadrilaterals by boundary construction method (also contains log and rez files) | Direct Construction | folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as | ||||||
| tiling m-file folder | folder of Matlab scripts to that draw tilings by triangles | |||||||||||||||||||||||||||||
| Boundary Construction | folder of Maple scripts to determine divisible quadrilaterals by boundary construction method (also contains log and rez files) | |||||||||||||||||||||||||||||
| Direct Construction | folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as | |||||||||||||||||||||||||||||
| tiling m-file folder | folder of Matlab scripts to that draw tilings by triangles | |||||||||||||||||||||||||||||
| Boundary Construction | folder of Maple scripts to determine divisible quadrilaterals by boundary construction method (also contains log and rez files) | |||||||||||||||||||||||||||||
| Direct Construction | folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as | |||||||||||||||||||||||||||||
| tiling m-file folder | folder of Matlab scripts to that draw tilings by triangles | |||||||||||||||||||||||||||||
| Boundary Construction | folder of Maple scripts to determine divisible quadrilaterals by boundary construction method (also contains log and rez files) | |||||||||||||||||||||||||||||
| Direct Construction | folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as | |||||||||||||||||||||||||||||
| tiling m-file folder | folder of Matlab scripts to that draw tilings by triangles | |||||||||||||||||||||||||||||
| Boundary Construction | folder of Maple scripts to determine divisible quadrilaterals by boundary construction method (also contains log and rez files) | |||||||||||||||||||||||||||||
| Direct Construction | folder containing Maple scripts to determine divisible quadrilaterals
by associated polygon methods (contains results as |
Geodesics, Length Spectrum of a
Surface and Billiards
| Scripts Folder | ||||||||||||||||||||||||||||||||||||||||
| Data Folder (reduced words for translations and glides) | ||||||||||||||||||||||||||||||||||||||||
| Images Folder (billiards, .eps files) | ||||||||||||||||||||||||||||||||||||||||
| NSchwartz.mws | numerical calculations for Schwartz triangles | billiardpics.mws | billiard drawing program for figures | billiardtest.mws | billiard drawing program with various tests | billiardsearch.mgm | Magma program to find gernating words for billiards | NSchwartz.mws | numerical calculations for Schwartz triangles | billiardpics.mws | billiard drawing program for figures | billiardtest.mws | billiard drawing program with various tests | billiardsearch.mgm | Magma program to find gernating words for billiards | NSchwartz.mws | numerical calculations for Schwartz triangles | billiardpics.mws | billiard drawing program for figures | billiardtest.mws | billiard drawing program with various tests | billiardsearch.mgm | Magma program to find gernating words for billiards | NSchwartz.mws | numerical calculations for Schwartz triangles | billiardpics.mws | billiard drawing program for figures | billiardtest.mws | billiard drawing program with various tests | billiardsearch.mgm | Magma program to find gernating words for billiards | ||||||||
| NSchwartz.mws | numerical calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||
| billiardpics.mws | billiard drawing program for figures | |||||||||||||||||||||||||||||||||||||||
| billiardtest.mws | billiard drawing program with various tests | |||||||||||||||||||||||||||||||||||||||
| billiardsearch.mgm | Magma program to find gernating words for billiards | |||||||||||||||||||||||||||||||||||||||
| NSchwartz.mws | numerical calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||
| billiardpics.mws | billiard drawing program for figures | |||||||||||||||||||||||||||||||||||||||
| billiardtest.mws | billiard drawing program with various tests | |||||||||||||||||||||||||||||||||||||||
| billiardsearch.mgm | Magma program to find gernating words for billiards | |||||||||||||||||||||||||||||||||||||||
| NSchwartz.mws | numerical calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||
| billiardpics.mws | billiard drawing program for figures | |||||||||||||||||||||||||||||||||||||||
| billiardtest.mws | billiard drawing program with various tests | |||||||||||||||||||||||||||||||||||||||
| billiardsearch.mgm | Magma program to find gernating words for billiards | |||||||||||||||||||||||||||||||||||||||
| NSchwartz.mws | numerical calculations for Schwartz triangles | |||||||||||||||||||||||||||||||||||||||
| billiardpics.mws | billiard drawing program for figures | |||||||||||||||||||||||||||||||||||||||
| billiardtest.mws | billiard drawing program with various tests | |||||||||||||||||||||||||||||||||||||||
| billiardsearch.mgm | Magma program to find gernating words for billiards |
Moduli
| Scripts Folder | ||||||||||
| permtoLFT.mws | permutation action on the quotient spaces | permtoLFT.mws | permutation action on the quotient spaces | permtoLFT.mws | permutation action on the quotient spaces | permtoLFT.mws | permutation action on the quotient spaces | ||
| permtoLFT.mws | permutation action on the quotient spaces | |||||||||
| permtoLFT.mws | permutation action on the quotient spaces | |||||||||
| permtoLFT.mws | permutation action on the quotient spaces | |||||||||
| permtoLFT.mws | permutation action on the quotient spaces |
Ovals and Oval Intersections
| Scripts Folder | ||||||||||||||||||||
| ovalfunc.mgm | oval intersection functions | ovalint.mgm | sample oval intersection calculations | ovalfunc.mgm | oval intersection functions | ovalint.mgm | sample oval intersection calculations | ovalfunc.mgm | oval intersection functions | ovalint.mgm | sample oval intersection calculations | ovalfunc.mgm | oval intersection functions | ovalint.mgm | sample oval intersection calculations | ||||
| ovalfunc.mgm | oval intersection functions | |||||||||||||||||||
| ovalint.mgm | sample oval intersection calculations | |||||||||||||||||||
| ovalfunc.mgm | oval intersection functions | |||||||||||||||||||
| ovalint.mgm | sample oval intersection calculations | |||||||||||||||||||
| ovalfunc.mgm | oval intersection functions | |||||||||||||||||||
| ovalint.mgm | sample oval intersection calculations | |||||||||||||||||||
| ovalfunc.mgm | oval intersection functions | |||||||||||||||||||
| ovalint.mgm | sample oval intersection calculations |
Separability of
Symmetries
| Scripts Folder |
||||
|
Separability of Symmetries
– uing graphs
| Scripts Folder, Data folder, Genus Data Folder |
||||||
|
Tilings with Matlab
The scripts in this folder allow one to create and draw triangular
tilings, according to a tiling word. The main scripts are mtess.m
for creating tiling words and ttess.m for drawing tilings according
to a word.
| Scripts Folder | ||||||||||||||||||||
| mtess.m | oval intersection functions | ttess.m | sample oval intersection calculations | mtess.m | oval intersection functions | ttess.m | sample oval intersection calculations | mtess.m | oval intersection functions | ttess.m | sample oval intersection calculations | mtess.m | oval intersection functions | ttess.m | sample oval intersection calculations | ||||
| mtess.m | oval intersection functions | |||||||||||||||||||
| ttess.m | sample oval intersection calculations | |||||||||||||||||||
| mtess.m | oval intersection functions | |||||||||||||||||||
| ttess.m | sample oval intersection calculations | |||||||||||||||||||
| mtess.m | oval intersection functions | |||||||||||||||||||
| ttess.m | sample oval intersection calculations | |||||||||||||||||||
| mtess.m | oval intersection functions | |||||||||||||||||||
| ttess.m | sample oval intersection calculations |
