Hollow small stellated dodecahedral antiprism

The hollow small stellated dodecahedral antiprism or hossdap is a prismatic scaliform polychoron that consists of 12 pentagrammic antiprisms and 24 pentagrammic pyramids. 5 pentagrammic antiprisms and 6 pentagrammic pyramids join at each vertex.

Hollow small stellated dodecahedral antiprism
(OFF file)
Rank	4
Type	Scaliform
Space	Spherical
Notation
Bowers style acronym	Hossdap
Coxeter diagram	ß2ß5o5/2o (hossdap + 2 degenerate cells)
Elements
Cells	24 pentagrammic pyramids, 12 pentagrammic antiprisms
Faces	120 triangles, 24 pentagrams
Edges	60+60
Vertices	24
Vertex figure	Pentagrammic cuploid, edge lengths (√5–1)/2 (pentagon), 1 (pentagram), 1 (lateral edges)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2} ≈ 0.70711$
Height	$\sqrt{\frac{\sqrt5-1}{2}} ≈ 0.78615$
Related polytopes
Army	Semi-uniform Ipe
Regiment	Hossdap
Dual	Hollow great dodecahedral antitegum
Convex core	Elongated dodecahedral tegum
Abstract & topological properties
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

It can be constructed as a holosnub great dodecahedral prism after coinciding base cells blend out.

Vertex coordinates

The vertices of a hollow small stellated dodecahedral antiprism of edge length 1 are given by all even permutations of the first three coordinates of:

• $\Biggl(0, \pm\frac{1}{2}, \pm\frac{\sqrt{5}-1}{4}, \pm\frac{\sqrt{2\sqrt{5}-2}}{4}\Biggr)$

Convex core

The convex core of this polychoron is an elongated dodecahedral tegum that consists of 12 pentagonal prisms (from the stap cells) and 24 pentagonal pyramids (from the stappy cells).

External links

• Bowers, Jonathan. "Category S1: Simple Scaliforms" (#S2).

• Klitzing, Richard. "hossdap".