Rectified small prismatodecachoron

Rectified small prismatodecachoron
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Respid
Coxeter diagram	uo3ox3xo3ou&#zq
Elements
Cells	20 triangular antiprisms, 10 octahedra, 20 rectified triangular prisms
Faces	120 isosceles triangles, 40+40 triangles, 300 squares
Edges	120+120
Vertices	60
Vertex figure	Isosceles trapezoidal prism
Measures (short edge length 1)
Edge lengths	Edges of triangles (120): 1
	Lacing edges (120): ${\sqrt {2}}\approx 1.41421$
Circumradius	${\sqrt {3}}\approx 1.73205$
Central density	1
Related polytopes
Army	Respid
Regiment	Respid
Dual	Joined triangular-antitegmatic icosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4×2, order 240
Convex	Yes
Nature	Tame

The rectified small prismatodecachoron or respid is a convex isogonal polychoron that consists of 10 octahedra, 20 rectified triangular prisms, and 20 triangular antiprisms. 1 octahedron, 3 rectified triangular prisms, and 2 triangular antiprisms join at each vertex. It can be formed by rectifying the small prismatodecachoron.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the small rhombated pentachoron, where the edges of the octahedra are half the length of the other edges. It is one of five polychora (including two transitional cases) formed from two small rhombated pentachora, and is the transitional point between the small birhombatodecachoron and medial birhombatodecachoron.

The ratio between the longest and shortest edges is 1:${\sqrt {2}}$ ≈ 1:1.41421.

External links

• Bowers, Jonathan. "Pennic and Decaic Isogonals".

• Klitzing, Richard. "respid".