Icositetrafold octaswirlchoron
Icositetrafold octaswirlchoron | |
---|---|
File:Icositetrafold octaswirlchoron.png | |
Rank | 4 |
Type | Isogonal |
Space | Spherical |
Elements | |
Cells | 288 rhombic disphenoids, 192 triangular gyroprisms |
Faces | 1152 scalene triangles, 192 triangles |
Edges | 144+288+576 |
Vertices | 144 |
Vertex figure | Edge-vertical bisected square gyrotegum |
Measures (circumradius 1) | |
Edge lengths | 8-valence (144): |
4-valence (288): | |
3-valence (576): | |
Central density | 1 |
Related polytopes | |
Dual | Cubiswirlic hecatontetracontatetrachoron |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B3●I2(24), order 1152 |
Convex | Yes |
Nature | Tame |
The icositetrafold octaswirlchoron is an isogonal polychoron with 192 triangular gyroprisms, 288 rhombic disphenoids, and 144 vertices. 8 triangular gyroprisms and 8 rhombic disphenoids join at each vertex. It is the sixth in an infinite family of isogonal octahedral swirlchora.
The ratio between the longest and shortest edges is 1: ≈ 1:3.05006.
Vertex coordinates[edit | edit source]
Coordinates for the vertices of an icositetrafold octaswirlchoron of circumradius 1, centered at the origin, are given by all permutations of:
defining an icositetrachoron, along with all permutations of:
defining the dual icositetrachoron, along with reflections through the x=y and z=w hyperplanes of:
along with reflections through the x=y and z=w hyperplanes and with all even sign changes of:
along with reflections through the x=y and z=w hyperplanes and with all odd sign changes of:
Isogonal derivatives[edit | edit source]
Substitution by vertices of these following elements will produce these convex isogonal polychora:
- Triangular gyroprism (192): Icositetrafold cubiswirlchoron
- Triangle (192): Icositetrafold cubiswirlchoron
- Edge (144): Icositetrafold octaswirlchoron