Toroidal blend of 92 dodecahedra

Toroidal blend of 92 dodecahedra
(3D model)
Rank	3
Type	Stewart toroid
Elements
Faces	12+12+60+60+60+60+60+60+120+120+120+120 pentagons
Edges	60+60+60+60+120 +60+60+60+60+120+120+120 +60+60+120+120+120+120+120+120+120+120+120
Vertices	60+60+60+60 +20+20+60+60+120+120 +60+60+120+120+120+120
Vertex figures	20+20+60+60+60+60+120+120+120+120 triangles, edge length (1+√5)/2
	60+60+120+120 [5.5.5.5]
	60+60 [5.5.5.5.5]
Measures (edge length 1)
Volume	$23\left(15+7{\sqrt {5}}\right)\approx 705.00694$
Surface area	$216{\sqrt {25+10{\sqrt {5}}}}\approx 1486.49247$
Central density	0
Related polytopes
Convex hull	Chamfered dodecahedron, edge lengths 1 (pentagon), ${\frac {\sqrt {10\left(25+11{\sqrt {5}}\right)}}{5}}$ (hexagon-hexagon)
Abstract & topological properties
Flag count	8640
Euler characteristic	–56
Orientable	Yes
Genus	29
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The toroidal blend of 92 dodecahedra is a Stewart toroid that consists of 864 pentagons. It can be obtained by outer-blending ninety-two dodecahedra together in eight-membered loops that resemble rhombi, forming a virtual rhombic triacontahedron. The thirty-two dodecahedra at the virtual polyhedron's vertices are all oriented in the same way.

Relations

Versions of the toroid can be made out of copies of most Archimedean and Johnson solids that share the faceplanes of the dodecahedron.

External links

• Doskey, Alex. "Chapter 7 - Exploration of (R)(A) Toroids".
• Miyazaki, Koji and Takada, Ichiro. "Uniform Ant-hills in the World of Golden Isozonohedra", figure 26(4)
• Parker, Matt. “Polygons of New York”.