# Elongated square bipyramid

The elongated square bipyramid is one of the 92 Johnson solids (J15). It consists of 8 triangles and 4 squares. It can be constructed by inserting a cube, seen as a square prism, between the two pyramidal halves of the regular octahedron, seen as a square bipyramid.

Elongated square bipyramid
Rank3
TypeCRF
Notation
Bowers style acronymEsquidpy
Coxeter diagramoxxo4oooo&#xt
Elements
Faces8 triangles, 4 squares
Edges4+8+8
Vertices2+8
Vertex figures2 squares, edge length 1
8 kites, edge lengths 1 and 2
Measures (edge length 1)
Volume${\displaystyle {\frac {3+{\sqrt {2}}}{3}}\approx 1.47140}$
Dihedral angles3–4: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
3–3: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
4–4: 90°
Central density1
Number of external pieces12
Level of complexity5
Related polytopes
ArmyEsquidpy
RegimentEsquidpy
DualSquare bifrustum
ConjugateNone
Abstract & topological properties
Flag count80
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryB2×A1, order 16
ConvexYes
NatureTame

## Vertex coordinates

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

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$ ,
• ${\displaystyle \left(0,\,0,\,\pm {\frac {1+{\sqrt {2}}}{2}}\right)}$ .

## Representations

An elongated square bipyramid has the following Coxeter diagrams:

• oxxo4oooo&#xt (full symmetry)
• oxxo oxxo&#xt (rectangular symmetry)
• xwx xox&#xt (rectangular axial)
• wx ox4oo&#zx (as tegum sum)
• x(xw)x o(qo)o&#xt (edge first)
• qoo oqo xxw&#zx (cuboid symmetry)