Elongated square pyramid

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Elongated square pyramid
Rank3
TypeCRF
Notation
Bowers style acronymEsquipy
Coxeter diagramoxx4ooo&#xt
Elements
Faces4 triangles, 1+4 squares
Edges4+4+4+4
Vertices1+4+4
Vertex figure1 square, edge length 1; 4 kites, edge lengths 1 and 2; 4 triangles, edge lengths 2
Measures (edge length 1)
Volume
Dihedral angles3–4:
 3–3:
 4–4: 90°
Central density1
Number of external pieces9
Level of complexity8
Related polytopes
ArmyEsquipy
RegimentEsquipy
DualElongated square pyramid
ConjugateRetroelongated square pyramid
Abstract & topological properties
Flag count64
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryB2×I, order 8
ConvexYes
NatureTame

The elongated square pyramid, sometimes called an augmented cube, is one of the 92 Johnson solids (J8). It consists of 4 triangles and 1+4 squares. It can be constructed by attaching a cube, seen as a square prism, to the base of the square pyramid.

If a second pyramid is attached to the opposite face of the cube, the result is the elongated square bipyramid.

Vertex coordinates[edit | edit source]

An elongated square pyramid of edge length 1 has the following vertices:

External links[edit | edit source]