# Hollow small stellated dodecahedral antiprism

(Redirected from Hossdap)
Hollow small stellated dodecahedral antiprism
Rank4
TypeScaliform
Notation
Bowers style acronymHossdap
Coxeter diagramß2ß5o5/2o (hossdap + 2 degenerate cells)
Elements
Cells24 pentagrammic pyramids, 12 pentagrammic antiprisms
Faces120 triangles, 24 pentagrams
Edges60+60
Vertices24
Vertex figurePentagrammic cuploid, edge lengths (5–1)/2 (pentagon), 1 (pentagram), 1 (lateral edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Height${\displaystyle {\sqrt {\frac {{\sqrt {5}}-1}{2}}}\approx 0.78615}$
Related polytopes
ArmySemi-uniform Ipe
RegimentHossdap
DualHollow great dodecahedral antitegum
Convex coreElongated dodecahedral tegum
Abstract & topological properties
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

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.

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:

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

## 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).