Excavated pentagonal orthobicupola

Excavated pentagonal orthobicupola
(3D model)
Rank	3
Type	Near-miss Stewart toroid
Elements
Faces	10 triangles, 10 squares, 5 rectangles
Edges	5+5+5+10+20
Vertices	10+10
Measures (outer edge length 1)
Height	${\sqrt {\frac {10-2{\sqrt {5}}}{5}}}\approx 1.05146$
Central density	0
Related polytopes
Army	Pobcu
Convex hull	Pentagonal orthobicupola
Abstract & topological properties
Surface	Torus
Orientable	Yes
Genus	1
Properties
Symmetry	H2×A1, order 20
Convex	No

The excavated pentagonal orthobicupola is a quasi-convex near-miss Stewart toroid. It is made by excavating a slightly non-uniform pentagonal prism from a pentagonal orthobicupola. It is a near-miss because the pentagonal orthobicupola has a height of slightly more than one so the excavated faces must be rectangles.

It is both quasi-convex and weakly convex.

Vertex coordinates

Its vertex coordinates are the same as those of the pentagonal orthobicupola.

Bibliography

• Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686-119 36-3.