Rectified decachoron

Rectified decachoron
(OFF file)
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Redeca
Coxeter diagram	xo3od3do3ox&#zh
Elements
Cells	30 tetragonal disphenoids, 10 rectified truncated tetrahedra
Faces	120 isosceles triangles, 20 triangles, 20 hexagons
Edges	60+120
Vertices	60
Vertex figure	Wedge
Measures (short edge length 1)
Edge lengths	Edges of triangles (60): 1
	Lacing edges (120): ${\sqrt {3}}\approx 1.73205$
Circumradius	${\sqrt {7}}\approx 2.64575$
Central density	1
Related polytopes
Army	Redeca
Regiment	Redeca
Dual	Joined bidecachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4×2, order 240
Convex	Yes
Nature	Tame

The rectified decachoron is a convex isogonal polychoron that consists of 10 rectified truncated tetrahedra and 30 tetragonal disphenoids. 3 rectified truncated tetrahedra and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the decachoron.

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 3 times 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 great birhombatodecachoron.

The ratio between the longest and shortest edges is 1:${\sqrt {3}}$ ≈ 1:1.73205.

External links

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

• Klitzing, Richard. "redeca".