Chapter 7. Case Studies

Table of Contents

Tetrahedron Stellation I (Deltoid)
Truncated Deltoid
Tetrahedron Iterated Stellation 3_1
Tetrahedron Stellation II
Tetrahedron Reticulated
Tetrahedron Reticulated (big)
Tetrahedron Reticulated (tall)
Tetrahedron Reticulated (huge)
Octahedron stellation II
Icosahedron
Standard (regular)
Variant 1
Icosahedron Stellation I
Icosahedron Stellation II
Cube Triang II
Yabi
Bipyramid Octa
L2(7)
Cartographic
Regular
M(24)
Torus 3x4
Trapezohedron
S(5)
A(6)
Quad Star
Reticulated 2x2 Cube
Reticulated 3x3 Cube Variants
standard Rubik's Cube
rotated corner
rotated 2x2 area
rotated 3x3 area
a follow up to variant 3
Rhombic Dodecahedron
Zonotope 5
Monkgau
Costa-Hoffman minimal surface
Quad Hex tesselation on a torus
Pentagonal Quasicrystals
Initial decagon
Iteration one
Iteration two
Iteration three
Iteration four
Heptagonal Quasicrystals
Initial 14-gon
DoubleDodecahedron
Icositetra
Dode Tor 6
Torus Hexa 3x5
Hexa Tor
Hexa UnOrient
Fancy Heptas
ToDo

Here various graphs are investigated. The classification is sometimes arbitrary, since a graph may arise as a result of different constructions (stellation, reticulation, truncation, glueing etc.). Some occuring mathematical terms will be explained later in subsequent chapters.

This graph arises as the stellation of a tetrahedron and is also known as a deltoid.


vertices: 8
faces: 12
edges: 18
genus: 0

characteristic polynomial:

dual's characteristic polynomial:

chromatic number: 3

lattice group: A4 × S3