Polyhedra Cut Locus Calculation

Visualize cut loci of the 2-d surfaces of polyhedra (paper available on arxiv)

Tested with Python 3.8.10 on Ubuntu (versions 20.04, 22.04, and 24.04) and on Windows 11

• Interactive Cut Locus Visualization:

  

• Path Unfolding Visualization:

  

• Voronoi Star Unfolding Visualization:

  

TABLE OF CONTENTS
Installation Instructions	instructions for how to set up code
Installation Test	test example (tetrahedron cut locus)
Cut Locus	instructions for running interactive cut locus visualization
Path Unfolding	instructions for running interactive path unfolding visualization
Implemented Shapes	list of implemented polyhedra and examples of their cut loci
Implement New Shapes	instructions to implement new shapes

Installation (assuming Python is installed)

• Option 1: Download zip, then extract all

  run the following in terminal/command prompt to install Python package:

  (replace <name of folder> with path of folder you extracted it to)

  cd <name of folder>
  pip3 install -e .

• Option 2: Clone Repository, then install the python package (assumes Git is installed)

  git clone https://github.com/pranavraj575/polyhedra_cut_locus
  pip3 install -e polyhedra_cut_locus

Installation Test

Run cut_locus.py from terminal/command prompt in the polyhedra_cut_locus folder

(move to correct folder with cd <name of folder>)

Example:

python3 cut_locus.py --shape tetrahedron --center-pt --legend 

To see the possible arguments, run the following:

python3 cut_locus.py -h

Note: try replacing python3 with python if you get error "Python was not found"

Cut Locus:

Run cut_locus.py from terminal/command prompt in the polyhedra_cut_locus folder

(move to correct folder with cd <name of folder>)

Example:

python3 cut_locus.py --shape tetrahedron --center-pt --legend 

Path Unfolding:

Run unfolding.py from terminal/command prompt in the polyhedra_cut_locus folder

Example:

python3 unfolding.py --shape cube

Voronoi Star Unfolding:

Same as path unfolding, with the additional argument --voronoi-star

Example:

python3 unfolding.py --shape octahedron --voronoi-star

Implemented shapes:

Platonic Solids

Includes all of the platonic solids.

• Tetrahedron:

  python3 cut_locus.py --shape tetrahedron
  python3 unfolding.py --shape tetrahedron --voronoi-star

  

• Cube:

  python3 cut_locus.py --shape cube

  

• Octahedron:

  python3 cut_locus.py --shape octahedron

  

• Dodecahedron:

  python3 cut_locus.py --shape dodecahedron --click
  python3 unfolding.py --shape dodecahedron --click --voronoi-star

  

• Icosahedron:

  python3 cut_locus.py --shape icosahedron --click
  python3 unfolding.py --shape icosahedron --click --voronoi-star

  

Archimedean Solids

Includes some of the archimedean solids.

• Truncated Tetrahedron:

  python3 cut_locus.py --shape trunc-tetrahedron

  

• Cuboctahedron:

  python3 cut_locus.py --shape cuboctahedron

  

• Truncated Cube:

  python3 cut_locus.py --shape trunc-cube

  

Polyhedra Families

• Prism:

  replace <n> with the n-gon you want (3<=n)

  python3 cut_locus.py --shape prism --n <n>

  

• Antiprism:

  replace <n> with the n-gon you want (2<=n)

  python3 cut_locus.py --shape antiprism --n <n>

  

• Pyramid:

  replace <n> with the n-gon you want (3<=n<=5)

  python3 cut_locus.py --shape pyramid --n <n>

  

• Elongated Pyramid:

  replace <n> with the n-gon you want (2<=n<=5)

  python3 cut_locus.py --shape longpyramid --n <n>

  

• Bipyramid:

  replace <n> with the n-gon you want (2<=n<=5)

  python3 cut_locus.py --shape bipyramid --n <n>

  

• Elongated Bipyramid:

  replace <n> with the n-gon you want (3<=n<=5)

  python3 cut_locus.py --shape longbipyramid --n <n>

  

Non-Polyhedra

Includes some non-polyhedra. The cut locus algorithm is not guaranteed to be correct for these implementations (though it seems to still work).

• Torus:

  python3 cut_locus.py --shape torus

  

• Mirror (two n-gons glued to each other):

  replace <n> with the n-gon you want (3<=n)

  python3 cut_locus.py --shape mirror --n <n>