Trishecatonicosachoron

Trishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Tahi
Coxeter diagram	o3o5x3x5/3*b ()
Elements
Cells	120 dodecahedra, 120 great stellated dodecahedra, 120 icosidodecadodecahedra
Faces	1440 pentagons, 1440 pentagrams, 1200 hexagons
Edges	3600+3600
Vertices	2400
Vertex figure	Crossed triangular frustum, edge lengths (√5–1)/2 (small base), (1+√5)/2 (large base), and √3 (sides)
Measures (edge length 1)
Circumradius	2
Hypervolume	${\frac {2475}{2}}=1237.5$
Dichoral angles	Ided–6–ided: 120°
	Ided–5–doe: 108°
	Ided–5/2–gissid: 36°
Number of external pieces	38520
Level of complexity	125
Related polytopes
Army	Sidpixhi, edge length ${\frac {3-{\sqrt {5}}}{2}}$
Regiment	Siddapady
Conjugate	Trishecatonicosachoron
Abstract & topological properties
Flag count	86400
Euler characteristic	–1080
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The trishecatonicosachoron, or tahi, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra, 120 great stellated dodecahedra, and 120 icosidodecadodecahedra. 1 dodecahedron, 1 great stellated dodecahedron, and 3 icosidodecadodecahedra join at each vertex.

Gallery

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the trishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#464).

• Klitzing, Richard. "tahi".