Toroidal blend of 38 octahedra

Toroidal blend of 38 octahedra
(3D model)
Rank	3
Type	Stewart toroid
Elements
Faces	8+8+24+24+24+24+48+48 triangles
Edges	24+24+24+24+24+48+48+48+48
Vertices	6+6+24+24+24
Vertex figures	6 squares, edge length 1
	6 (3.3.3)4
	24 (3.3.3)2
	24 (3.3.3.3)2 (reflection-symmetric)
	24 (3.3.3.3)2 (rectangular-symmetric)
Measures (edge length 1)
Volume	${\frac {38{\sqrt {2}}}{3}}\approx 17.91337$
Surface area	$52{\sqrt {3}}\approx 90.06664$
Central density	0
Related polytopes
Convex hull	Chamfered octahedron
Abstract & topological properties
Flag count	1248
Euler characteristic	–20
Orientable	Yes
Genus	11
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The toroidal blend of 38 octahedra is a Stewart toroid that consists of 208 triangles. It can be obtained by outer-blending thirty-eight octahedra together in eight-membered loops that resemble rhombi, forming a virtual rhombic dodecahedron. The 14 octahedra at the virtual polyhedron's vertices are all oriented in the same way; the other 24 serve as triangular antiprisms.

Relations

The toroid can be made out of copies of most other Platonic, Archimedean, or Johnson solids that share the faceplanes of the octahedron, including the icosahedron and some of its truncations.

Gallery

External links

• Doskey, Alex. "Chapter 7 - Exploration of (R)(A) Toroids".