Pentagrammic pyramid

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Pentagrammic pyramid
Rank3
TypeSegmentotope
Notation
Bowers style acronymStappy
Coxeter diagramox5/2oo&#x
Elements
Faces5 triangles, 1 pentagram
Edges5+5
Vertices1+5
Vertex figures1 pentagram, edge length 1
 5 isosceles triangles, edge lengths 1, 1, (5-1)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3-5/2:
 3-3:
Height
Related polytopes
ArmyNon-RF peppy, edge lengths (base), 1 (sides)
RegimentStappy
DualPentagrammic pyramid
ConjugatePentagonal pyramid
Convex corePentagonal pyramid
Abstract & topological properties
Flag count40
OrientableYes
Properties
SymmetryH2×I, order 10
ConvexNo
NatureTame

The pentagrammic pyramid, or stappy, is a pyramid with a pentagrammic base and 5 triangles as sides.

It is the vertex-first cap of the great icosahedron. A regular great icosahedron can be constructed by attaching two pentagrammic pyramids to the bases of a pentagrammic retroprism.

Vertex coordinates[edit | edit source]

A pentagrammic pyramid of edge length 1 has the following vertices:

Related polyhedra[edit | edit source]

Two pentagrammic pyramids can be attached at their bases to form a pentagrammic tegum.

External links[edit | edit source]