Medial retroditetrahedronary trishecatonicosachoron

Medial retroditetrahedronary trishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Mardatathi
Elements
Cells	120 great stellated dodecahedra, 120 great ditrigonary icosidodecahedra, 120 dodecadodecahedra
Faces	1200 triangles, 1440 pentagons, 1440 pentagrams
Edges	3600
Vertices	600
Measures (edge length 1)
Circumradius	${\sqrt {2}}\approx 1.41421$
Hypervolume	$5{\frac {185+9{\sqrt {5}}}{4}}\approx 256.40576$
Dichoral angles	Gidtid–3–gidtid: 120°
	Gissid–5/2–did: 72°
	Ditdid–5–did: 72°
Number of external pieces	31320
Level of complexity	63
Related polytopes
Army	Hi, edge lenght ${\frac {3-{\sqrt {5}}}{2}}$
Regiment	Dattady
Conjugate	Retroinverted ditetrahedronary trishecatonicosachoron
Abstract & topological properties
Flag count	72000
Euler characteristic	720
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The medial retroditetrahedronary trishecatonicosachoron, or mardatathi, is a nonconvex uniform polychoron that consists of 120 great ditrigonary icosidodecahedra, 120 great stellated dodecahedra, and 120 dodecadodecahedra. Four great ditrigonary icosidodecahedra, four great stellated dodecahedra, and six dodecadodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#820).

• Klitzing, Richard. "mardatathi".