Images & Archives

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 surfacegenus2.gifgenus2.eps
icosahedral tiling of sphereicos.gificos.eps
(2,4,4) tiling on a torustorus244.giftorus244.eps
(3,3,3) tiling on a torustorus333.giftorus333.eps

Hyperbolic tilings

Images in the table below are stored in this Google Drive images folder

(2,4,5)- tiling of the hyperbolic planett245.gif 
(2,5,5)- tiling of the hyperbolic plane tt255.gif 
(3,5,5)- tiling of the hyperbolic planet355.gif 
(4,3,3)- tiling of the hyperbolic planet433.gif 

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:


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

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretationimage
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretationimage
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretationimage
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretationimage
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretationimage
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretation
image
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretation
image
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretation
image
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretation
image
scripts

 

various constructions

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
files (text)

.log transcript file

.eps encapsulated post script

Background
Notes
Research
Project Areas
File Extension Interpretation
image
scripts

 

various constructions

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
files (text)

.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.mwsicosahedral tiling of the spheretorus244.mws(2,4,4) tiling on the torustorus333.mws(3,3,3) tiling on the torusgenus2.mwssurface of genus twotriang4.mwsmaster tile (needs gtools.mpl)icos.mwsicosahedral tiling of the spheretorus244.mws(2,4,4) tiling on the torustorus333.mws(3,3,3) tiling on the torusgenus2.mwssurface of genus twotriang4.mwsmaster tile (needs gtools.mpl)icos.mwsicosahedral tiling of the spheretorus244.mws(2,4,4) tiling on the torustorus333.mws(3,3,3) tiling on the torusgenus2.mwssurface of genus twotriang4.mwsmaster tile (needs gtools.mpl)icos.mwsicosahedral tiling of the spheretorus244.mws(2,4,4) tiling on the torustorus333.mws(3,3,3) tiling on the torusgenus2.mwssurface of genus twotriang4.mwsmaster tile (needs gtools.mpl)
icos.mwsicosahedral tiling of the sphere
torus244.mws(2,4,4) tiling on the torus
torus333.mws(3,3,3) tiling on the torus
genus2.mwssurface of genus two
triang4.mwsmaster tile (needs gtools.mpl)
icos.mwsicosahedral tiling of the sphere
torus244.mws(2,4,4) tiling on the torus
torus333.mws(3,3,3) tiling on the torus
genus2.mwssurface of genus two
triang4.mwsmaster tile (needs gtools.mpl)
icos.mwsicosahedral tiling of the sphere
torus244.mws(2,4,4) tiling on the torus
torus333.mws(3,3,3) tiling on the torus
genus2.mwssurface of genus two
triang4.mwsmaster tile (needs gtools.mpl)
icos.mwsicosahedral tiling of the sphere
torus244.mws(2,4,4) tiling on the torus
torus333.mws(3,3,3) tiling on the torus
genus2.mwssurface of genus two
triang4.mwsmaster 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.mwsGeometric constructionsDHgeom.mwsInvariance and distance calculations for the
disc
UHgeom.mwsInvariance and distance calculations for the
upper half plane
NSchwartz.mwsNumerical calculations for Schwartz trianglesschwartz.mwsSymbolic Calculations for Schwartz trianglesHgeom.mwsGeometric constructionsDHgeom.mwsInvariance and distance calculations for the
disc
UHgeom.mwsInvariance and distance calculations for the
upper half plane
NSchwartz.mwsNumerical calculations for Schwartz trianglesschwartz.mwsSymbolic Calculations for Schwartz trianglesHgeom.mwsGeometric constructionsDHgeom.mwsInvariance and distance calculations for the
disc
UHgeom.mwsInvariance and distance calculations for the
upper half plane
NSchwartz.mwsNumerical calculations for Schwartz trianglesschwartz.mwsSymbolic Calculations for Schwartz trianglesHgeom.mwsGeometric constructionsDHgeom.mwsInvariance and distance calculations for the
disc
UHgeom.mwsInvariance and distance calculations for the
upper half plane
NSchwartz.mwsNumerical calculations for Schwartz trianglesschwartz.mwsSymbolic Calculations for Schwartz triangles
Hgeom.mwsGeometric constructions
DHgeom.mwsInvariance and distance calculations for the
disc
UHgeom.mwsInvariance and distance calculations for the
upper half plane
NSchwartz.mwsNumerical calculations for Schwartz triangles
schwartz.mwsSymbolic Calculations for Schwartz triangles
Hgeom.mwsGeometric constructions
DHgeom.mwsInvariance and distance calculations for the
disc
UHgeom.mwsInvariance and distance calculations for the
upper half plane
NSchwartz.mwsNumerical calculations for Schwartz triangles
schwartz.mwsSymbolic Calculations for Schwartz triangles
Hgeom.mwsGeometric constructions
DHgeom.mwsInvariance and distance calculations for the
disc
UHgeom.mwsInvariance and distance calculations for the
upper half plane
NSchwartz.mwsNumerical calculations for Schwartz triangles
schwartz.mwsSymbolic Calculations for Schwartz triangles
Hgeom.mwsGeometric constructions
DHgeom.mwsInvariance and distance calculations for the
disc
UHgeom.mwsInvariance and distance calculations for the
upper half plane
NSchwartz.mwsNumerical calculations for Schwartz triangles
schwartz.mwsSymbolic 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

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

abelian2.act

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

abelian2.act

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

abelian2.act

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

abelian2.act

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

abelian2.act

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

abelian2.act

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

abelian2.act

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

abelian2.act

 

cyclic.act

perm.act

pgroupNA.act

solvableNANP.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
actions

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

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmsample script to find (2,3,5) – tilings of the
sphere with G = Alt(5),
tileclass.mgmfunction library for computing tilings and
calculating “theta”
tilerun.mgm

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmsample script to find (2,3,5) – tilings of the
sphere with G = Alt(5),
tileclass.mgmfunction library for computing tilings and
calculating “theta”
tilerun.mgm

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmsample script to find (2,3,5) – tilings of the
sphere with G = Alt(5),
tileclass.mgmfunction library for computing tilings and
calculating “theta”
tilerun.mgm

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmsample script to find (2,3,5) – tilings of the
sphere with G = Alt(5),
tileclass.mgmfunction library for computing tilings and
calculating “theta”
tilerun.mgm

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmsample script to find (2,3,5) – tilings of the
sphere with G = Alt(5),
tileclass.mgmfunction library for computing tilings and
calculating “theta”
tilerun.mgm

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmsample script to find (2,3,5) – tilings of the
sphere with G = Alt(5),
tileclass.mgmfunction library for computing tilings and
calculating “theta”
tilerun.mgm

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmsample script to find (2,3,5) – tilings of the
sphere with G = Alt(5),
tileclass.mgmfunction library for computing tilings and
calculating “theta”
tilerun.mgm

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmsample script to find (2,3,5) – tilings of the
sphere with G = Alt(5),
tileclass.mgmfunction library for computing tilings and
calculating “theta”
tilerun.mgm

 

abelian2.mgm

cyclic.mgm

perm.mgm

pgroupNA.mgm

solvableNANP.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.mgmfunction library for computing
tilings and calculating “theta”
quadrun.mgmmaster driver for
tiling classification program
quadclass.mgmfunction library for computing
tilings and calculating “theta”
quadrun.mgmmaster driver for
tiling classification program
quadclass.mgmfunction library for computing
tilings and calculating “theta”
quadrun.mgmmaster driver for
tiling classification program
quadclass.mgmfunction library for computing
tilings and calculating “theta”
quadrun.mgmmaster driver for
tiling classification program
quadclass.mgmfunction library for computing
tilings and calculating “theta”
quadrun.mgmmaster driver for
tiling classification program
quadclass.mgmfunction library for computing
tilings and calculating “theta”
quadrun.mgmmaster driver for
tiling classification program
quadclass.mgmfunction library for computing
tilings and calculating “theta”
quadrun.mgmmaster driver for
tiling classification program
quadclass.mgmfunction library for computing
tilings and calculating “theta”
quadrun.mgmmaster driver for
tiling classification program
Branching data
Data
and Script Folder
bradatpoly.mws branching
data for small polygons and low genus
bradatpoly.mwsbranching
data for small polygons and low genus
bradatpoly.mwsbranching
data for small polygons and low genus
bradatpoly.mwsbranching
data for small polygons and low genus
bradatpoly.mwsbranching
data for small polygons and low genus
bradatpoly.mwsbranching
data for small polygons and low genus
bradatpoly.mwsbranching
data for small polygons and low genus
bradatpoly.mwsbranching
data for small polygons and low genus
bradatpoly.mwsbranching
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
Imagesfolder 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
Imagesfolder 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
Imagesfolder 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
Imagesfolder 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
Imagesfolder 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
Imagesfolder 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
Imagesfolder 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
Imagesfolder 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
.mpl files)

tiling m-file folderfolder 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
.mpl files)

tiling m-file folderfolder 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
.mpl files)

tiling m-file folderfolder 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
.mpl files)

tiling m-file folderfolder 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
.mpl files)

tiling m-file folderfolder 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
.mpl files)

tiling m-file folderfolder 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
.mpl files)

tiling m-file folderfolder 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
.mpl files)

tiling m-file folderfolder 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
.mpl files)

Geodesics, Length Spectrum of a
Surface and Billiards

Scripts
Folder
Data
Folder
(reduced words for translations and glides)
Images
Folde
r (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.mwsnumerical calculations for Schwartz trianglesbilliardpics.mwsbilliard drawing program for figuresbilliardtest.mwsbilliard drawing program with various testsbilliardsearch.mgmMagma program to find gernating words for
billiards
NSchwartz.mwsnumerical calculations for Schwartz trianglesbilliardpics.mwsbilliard drawing program for figuresbilliardtest.mwsbilliard drawing program with various testsbilliardsearch.mgmMagma program to find gernating words for
billiards
NSchwartz.mwsnumerical calculations for Schwartz trianglesbilliardpics.mwsbilliard drawing program for figuresbilliardtest.mwsbilliard drawing program with various testsbilliardsearch.mgmMagma program to find gernating words for
billiards
NSchwartz.mwsnumerical calculations for Schwartz trianglesbilliardpics.mwsbilliard drawing program for figuresbilliardtest.mwsbilliard drawing program with various testsbilliardsearch.mgmMagma program to find gernating words for
billiards
NSchwartz.mwsnumerical calculations for Schwartz triangles
billiardpics.mwsbilliard drawing program for figures
billiardtest.mwsbilliard drawing program with various tests
billiardsearch.mgmMagma program to find gernating words for
billiards
NSchwartz.mwsnumerical calculations for Schwartz triangles
billiardpics.mwsbilliard drawing program for figures
billiardtest.mwsbilliard drawing program with various tests
billiardsearch.mgmMagma program to find gernating words for
billiards
NSchwartz.mwsnumerical calculations for Schwartz triangles
billiardpics.mwsbilliard drawing program for figures
billiardtest.mwsbilliard drawing program with various tests
billiardsearch.mgmMagma program to find gernating words for
billiards
NSchwartz.mwsnumerical calculations for Schwartz triangles
billiardpics.mwsbilliard drawing program for figures
billiardtest.mwsbilliard drawing program with various tests
billiardsearch.mgmMagma program to find gernating words for
billiards

Moduli

Scripts
Folder
permtoLFT.mws permutation action on the quotient
spaces
permtoLFT.mwspermutation action on the quotient
spaces
permtoLFT.mwspermutation action on the quotient
spaces
permtoLFT.mwspermutation action on the quotient
spaces
permtoLFT.mwspermutation action on the quotient
spaces
permtoLFT.mwspermutation action on the quotient
spaces
permtoLFT.mwspermutation action on the quotient
spaces
permtoLFT.mwspermutation action on the quotient
spaces
permtoLFT.mwspermutation action on the quotient
spaces

 

Ovals and Oval Intersections

Scripts
Folder
ovalfunc.mgm oval intersection functions
ovalint.mgm sample oval intersection calculations
ovalfunc.mgmoval intersection functionsovalint.mgmsample oval intersection calculationsovalfunc.mgmoval intersection functionsovalint.mgmsample oval intersection calculationsovalfunc.mgmoval intersection functionsovalint.mgmsample oval intersection calculationsovalfunc.mgmoval intersection functionsovalint.mgmsample oval intersection calculations
ovalfunc.mgmoval intersection functions
ovalint.mgmsample oval intersection calculations
ovalfunc.mgmoval intersection functions
ovalint.mgmsample oval intersection calculations
ovalfunc.mgmoval intersection functions
ovalint.mgmsample oval intersection calculations
ovalfunc.mgmoval intersection functions
ovalint.mgmsample oval intersection calculations

Separability of
Symmetries

Scripts
Folder
IsSplit.mgm determines whether a tiling is split
IsSplitS.mgm a tweaked version of IsSplit.mgm

Separability of Symmetries
– uing graphs

Scripts
Folder
, Data
folder
, Genus
Data Folder
Group.mgm Compute separability for all
reflections for a given group, using Reflective
Walk Algorithm
GroupS.mgm Compute separability for all reflections for a
given group, using modified Reflective Walk
Algorithm
Graph.mgm Compute separability for all reflections for a
given group, using Cayley Line Graph

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.moval intersection functionsttess.msample oval intersection calculationsmtess.moval intersection functionsttess.msample oval intersection calculationsmtess.moval intersection functionsttess.msample oval intersection calculationsmtess.moval intersection functionsttess.msample oval intersection calculations
mtess.moval intersection functions
ttess.msample oval intersection calculations
mtess.moval intersection functions
ttess.msample oval intersection calculations
mtess.moval intersection functions
ttess.msample oval intersection calculations
mtess.moval intersection functions
ttess.msample oval intersection calculations