# Square cupolic prism

Square cupolic prism
Rank4
TypeSegmentotope
Notation
Bowers style acronymSquacupe
Coxeter diagramxx ox4xx&#x
Elements
Cells4 triangular prisms, 1+4 cubes, 2 square cupolas, 1 octagonal prism
Faces8 triangles, 2+4+4+4+8+8 squares, 2 octagons
Edges4+8+8+8+8+16
Vertices8+16
Vertex figures8 isosceles trapezoidal pyramids, base edge lengths 1, 2, 2, 2, side edge length 2
16 irregular tetrahedra, edge lengths 1 (1), 2 (4), and 2+2 (1)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {3+{\sqrt {2}}}{2}}}\approx 1.48563}$
Hypervolume${\displaystyle {\frac {3+2{\sqrt {2}}}{3}}\approx 1.94281}$
Dichoral anglestrip–4–cube: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }}$
Cube–4–cube: 135º
Squacu–4–trip: 90°
Squacu–4–cube: 90°
Squacu–8–op: 90°
Trip–4–op: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Cube–4–op: 45°
HeightsSquacu atop squacu: 1
Cube atop op: ${\displaystyle {\frac {\sqrt {6}}{3}}\approx 0.81650}$
Central density1
Related polytopes
ArmySquacupe
RegimentSquacupe
DualSemibisected tetragonal trapezohedral tegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB2×A1×I, order 16
ConvexYes
NatureTame

The square cupolic prism, or squacupe, is a CRF segmentochoron (designated K-4.69 on Richard Klitzing's list). It consiss of 2 square cupolas, 4 triangular prisms, 1+4 cubes, and 1 octagonal prism.

As the name suggests, it is a prism based on the square cupola. As such, it is a segmentochoron between two square cupolas. It can also be viewed as a segmentochoron between an octagonal prism and a cube.

Two square cupolic prisms can be attached to opposite octagonal prismatic cells of the square-octagonal duoprism to produce a small rhombicuboctahedral prism.

## Vertex coordinates

Coordinates of the vertices of a square cupolic prism of edge length 1 centered at the origin are given by:

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