# Square orthobicupola

Square orthobicupola
Rank3
TypeCRF
Notation
Bowers style acronymSquobcu
Coxeter diagramxxx4oxo&#xt
Elements
Faces8 triangles, 2+8 squares
Edges4+4+8+16
Vertices8+8
Vertex figures8 isosceles trapezoids, edge lengths 1, 2, 2, 2
8 kites, edge lengths 1 and 2
Measures (edge length 1)
Volume${\displaystyle {\frac {6+4{\sqrt {2}}}{3}}\approx 3.88562}$
Dihedral angles3–4: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
4–4 cupolaic: 135°
3–3: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
4–4 join: 90°
Central density1
Number of external pieces18
Level of complexity8
Related polytopes
ArmySquobcu
RegimentSquobcu
Abstract & topological properties
Flag count128
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryB2×A1, order 16
ConvexYes
NatureTame

The square orthobicupola is one of the 92 Johnson solids (J28). It consists of 8 triangles and 2+8 squares. It can be constructed by attaching two square cupolas at their octagonal bases, such that the two square bases are in the same orientation.

If the cupolas are joined such that the bases are rotated 45°, the result is the square gyrobicupola.

## Vertex coordinates

A square orthobicupola of edge length 1 has vertices given by the following coordinates:

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

## Related polyhedra

An octagonal prism can be inserted between the two halves of the square orthobicupola to produce the elongated square orthobicupola, better known as the uniform small rhombicuboctahedron.