Small ditrigonal dodecicosidodecahedron

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Small ditrigonal dodecicosidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymSidditdid
Coxeter diagramx5/3o3x5*a ()
Elements
Faces20 triangles, 12 pentagrams, 12 decagons
Edges60+60
Vertices60
Vertex figureCrossed isosceles trapezoid, edge lengths 1, (5+5)/2, (5–1)/2, (5+5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3–10:
 5/2–10:
Central density4
Number of external pieces212
Level of complexity13
Related polytopes
ArmySemi-uniform Srid, edge lengths (pentagons), 1 (triangles)
RegimentSiid
DualSmall ditrigonal dodecacronic hexecontahedron
ConjugateGreat ditrigonal dodecicosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count480
Euler characteristic–16
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The small ditrigonal dodecicosidodecahedron, or sidditdid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 12 decagons. One triangle, one pentagram, and two decagons join at each vertex.

It is a faceting of the small icosicosidodecahedron, using its 12 pentagrams and 20 triangles along with 12 additional decagons.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the small icosicosidodecahedron.

Related polyhedra[edit | edit source]

o5/3o3o5*a truncations
Name OBSA CD diagram Picture
Ditrigonary dodecadodecahedron ditdid
Small complex icosidodecahedron (degenerate, ike+gad) cid
Great complex icosidodecahedron (degenerate, sissid+gike) gacid
Icosidodecadodecahedron ided
Small ditrigonal dodecicosidodecahedron sidditdid
Great ditrigonal dodecicosidodecahedron gidditdid
Icosidodecatruncated icosidodecahedron idtid
Snub icosidodecadodecahedron sided


External links[edit | edit source]