Swirlprismatodiminished rectified icositetrachoron

Swirlprismatodiminished rectified icositetrachoron
	(OFF file)
Rank	4
Type	Isogonal
Space	Spherical
Notation
Bowers style acronym	Spidrico
Elements
Cells	24 triangular prisms, 24 triangular antiprisms, 24 chiral rectified triangular prisms
Faces	144 isosceles triangles, 24+48 triangles, 72 rectangles
Edges	72+72+144
Vertices	72
Vertex figure	Triangular-ridge expanded tetragonal antiwedge
Measures (derived from unit-edged rectified icositetrachoron)
Edge lengths	3-valence (72): 1
	4-valence (72): 1
	3-valence (144):
Circumradius
Central density	1
Related polytopes
Dual	Swirlprismatostellated joined icositetrachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A3●G2, order 144
Convex	Yes
Nature	Tame

The swirlprismatodiminished rectified icositetrachoron or spidrico is an isogonal polychoron with 24 chiral rectified triangular prisms, 24 triangular prisms, 24 triangular antiprisms, and 72 vertices. 3 chiral rectified triangular prisms, 2 triangular antiprisms, and 2 triangular prisms join at each vertex. It can be constructed by removing the 24 vertices of an inscribed icositetrachoron of edge length $\sqrt3$ from a rectified icositetrachoron. In doing so the cuboctahedral cells have 3 vertices removed, while the cubes have 2 opposite corners removed and additional triangular prisms come in as the original's vertex figures.

The ratio between the longest and shortest edges is 1: $\sqrt2$ ≈ 1:1.41421.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a swirlprismatodiminished rectified icositetrachoron of circumradius $\sqrt3$ , centered at the origin, are given by:

$±\left(\frac{\sqrt3}{3},\,0,\,\sqrt2,\,\frac{\sqrt6}{3}\right),$
$±\left(-\frac{\sqrt3}{6},\,±\frac12,\,\sqrt2,\,\frac{\sqrt6}{3}\right),$
$±\left(0,\,1,\,\sqrt2,\,0\right),$
$±\left(±\frac{\sqrt3}{2},\,-\frac12,\,\sqrt2,\,0\right),$
$±\left(-\frac{\sqrt3}{3},\,0,\,\sqrt2,\,-\frac{\sqrt6}{3}\right),$
$±\left(\frac{\sqrt3}{6},\,±\frac12,\,\sqrt2,\,-\frac{\sqrt6}{3}\right),$
$±\left(0,\,-1,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{2}\right),$
$±\left(±\frac{\sqrt3}{2},\,\frac12,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{2}\right),$
$±\left(\frac{\sqrt3}{6},\,\frac32,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$
±\frac{\sqrt3}{6},\,-\frac32,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),</math>
$±\left(\frac{2\sqrt3}{3},\,1,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$
$±\left(\frac{2\sqrt3}{3},\,-1,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$
$±\left(-\frac{5\sqrt3}{6},\,\frac12,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$
$±\left(-\frac{5\sqrt3}{6},\,-\frac12,\,\frac{\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$
$±\left(-\frac{\sqrt3}{6},\,\frac32,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$
±{-\frac{\sqrt3}{6},\,-\frac32,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),</math>
$±\left(-\frac{2\sqrt3}{3},\,1,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$
$±\left(-\frac{2\sqrt3}{3},\,-1,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$
$±\left(\frac{5\sqrt3}{6},\,\frac12,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$
$±\left(\frac{5\sqrt3}{6},\,-\frac12,\,\frac{\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$
$±\left(-\frac{\sqrt3}{3},\,0,\,0,\,\frac{2\sqrt6}{3}\right),$
$±\left(\frac{\sqrt3}{6},\,±\frac12,\,0,\,\frac{2\sqrt6}{3}\right),$
$±\left(-\frac{\sqrt3}{6},\,\frac32,\,0,\,\frac{\sqrt6}{3}\right),$
±{-\frac{\sqrt3}{6},\,-\frac32,\,0,\,\frac{\sqrt6}{3}\right),</math>
$±\left(-\frac{2\sqrt3}{3},\,1,\,0,\,\frac{\sqrt6}{3}\right),$
$±\left(-\frac{2\sqrt3}{3},\,-1,\,0,\,\frac{\sqrt6}{3}\right),$
$±\left(\frac{5\sqrt3}{6},\,\frac12,\,0,\,\frac{\sqrt6}{3}\right),$
$±\left(\frac{5\sqrt3}{6},\,-\frac12,\,0,\,\frac{\sqrt6}{3}\right),$
$±\left(\frac{\sqrt3}{6},\,\frac32,\,0,\,-\frac{\sqrt6}{3}\right),$
±\frac{\sqrt3}{6},\,-\frac32,\,0,\,-\frac{\sqrt6}{3}\right),</math>
$±\left(\frac{2\sqrt3}{3},\,1,\,0,\,-\frac{\sqrt6}{3}\right),$
$±\left(\frac{2\sqrt3}{3},\,-1,\,0,\,-\frac{\sqrt6}{3}\right),$
$±\left(-\frac{5\sqrt3}{6},\,\frac12,\,0,\,-\frac{\sqrt6}{3}\right),$
$±\left(-\frac{5\sqrt3}{6},\,-\frac12,\,0,\,-\frac{\sqrt6}{3}\right).$