# Small ditrigonary icosidodecahedral antiprism

(Redirected from Sidtidap)
Small ditrigonary icosidodecahedral antiprism
Rank4
TypeUniform
Notation
Bowers style acronymSidtidap
Coxeter diagramβ2β5o3o ()
Elements
Cells40 tetrahedra, 12 pentagrammic antiprisms, 2 small ditrigonary icosidodecahedra
Faces40+120 triangles, 24 pentagrams
Edges60+120
Vertices40
Vertex figureTriangular cupola, edge lengths (5–1)/2 (3 base edges), 1 (remaining edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106}$
Hypervolume${\displaystyle {\frac {\sqrt {110+85{\sqrt {5}}}}{8}}\approx 2.16530}$
Dichoral anglesTet–3–stap: ${\displaystyle \arccos \left(-{\sqrt {\frac {5+3{\sqrt {5}}}{20}}}\right)\approx 139.91776^{\circ }}$
Sidtid–3–tet: ${\displaystyle \arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{2}}\right)\approx 105.66967^{\circ }}$
Sidtid–5/2–stap: 90°
Height${\displaystyle {\sqrt {\frac {{\sqrt {5}}-1}{2}}}\approx 0.78615}$
Number of external pieces174
Level of complexity32
Related polytopes
ArmySemi-uniform Dope
RegimentSidtidap
DualSmall triambic icosahedral antitegum
ConjugateNone
Abstract & topological properties
Euler characteristic–10
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small ditrigonary icosidodecahedral antiprism or sidtidap, is a nonconvex uniform polychoron that consists of 2 small ditrigonary icosidodecahedra, 12 pentagrammic antiprisms, and 40 tetrahedra. Each vertex joins 1 small ditrigonary icosidodecahedron, 3 pentagrammic antiprisms, and 4 tetrahedra.

It can be obtained as a holosnub dodecahedral prism.

## Vertex coordinates

The vertices of a small ditrigonary icosidodecahedral antiprism of edge length 1 are given by:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\sqrt {\frac {{\sqrt {5}}-1}{8}}}\right),}$

along with all even permutations of the first three coordinates of:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,0,\,\pm {\sqrt {\frac {{\sqrt {5}}-1}{8}}}\right).}$

## Related polychora

The regiment of the small ditrigonary icosidodecahedral antiprism also includes the ditrigonary dodecadodecahedral antiprism and the great ditrigonary icosidodecahedral antiprism.

The small icosicosidodecahedral alterprism is a partial Stott expansion of this polychoron.