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 nonsolvable rotation group actions nonabelian pgroup rotation group actions nonabelian nonpgroup solvable rotation group  abelian2.act
 two generator abelian rotation group actions
cyclic group rotation group actions nonsolvable rotation group actions nonabelian pgroup rotation group actions nonabelian nonpgroup solvable rotation group  abelian2.act
 two generator abelian rotation group actions
cyclic group rotation group actions nonsolvable rotation group actions nonabelian pgroup rotation group actions nonabelian nonpgroup solvable rotation group  abelian2.act
 two generator abelian rotation group actions
cyclic group rotation group actions nonsolvable rotation group actions nonabelian pgroup rotation group actions nonabelian nonpgroup solvable rotation group  
abelian2.act
 two generator abelian rotation group actions
cyclic group rotation group actions nonsolvable rotation group actions nonabelian pgroup rotation group actions nonabelian nonpgroup solvable rotation group  
abelian2.act
 two generator abelian rotation group actions
cyclic group rotation group actions nonsolvable rotation group actions nonabelian pgroup rotation group actions nonabelian nonpgroup solvable rotation group  
abelian2.act
 two generator abelian rotation group actions
cyclic group rotation group actions nonsolvable rotation group actions nonabelian pgroup rotation group actions nonabelian nonpgroup solvable rotation group  
abelian2.act
 two generator abelian rotation group actions
cyclic group rotation group actions nonsolvable rotation group actions nonabelian pgroup rotation group actions nonabelian nonpgroup 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 nonsolvable rotation groups (permutation group format) find nonabelian pgroup rotation groups (PC format) find nonabelian nonpgroup 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 nonsolvable rotation groups (permutation group format) find nonabelian pgroup rotation groups (PC format) find nonabelian nonpgroup 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 nonsolvable rotation groups (permutation group format) find nonabelian pgroup rotation groups (PC format) find nonabelian nonpgroup 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 nonsolvable rotation groups (permutation group format) find nonabelian pgroup rotation groups (PC format) find nonabelian nonpgroup 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 nonsolvable rotation groups (permutation group format) find nonabelian pgroup rotation groups (PC format) find nonabelian nonpgroup 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 nonsolvable rotation groups (permutation group format) find nonabelian pgroup rotation groups (PC format) find nonabelian nonpgroup 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 nonsolvable rotation groups (permutation group format) find nonabelian pgroup rotation groups (PC format) find nonabelian nonpgroup 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 nonsolvable rotation groups (permutation group format) find nonabelian pgroup rotation groups (PC format) find nonabelian nonpgroup 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 mfile 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 mfile 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 mfile 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 mfile 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 mfile 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 mfile 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 mfile 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 mfile 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 