Cubic cupola

In 4-dimensional geometry, the cubic cupola is a 4-polytope bounded by a rhombicuboctahedron, a parallel cube, connected by 6 square prisms, 12 triangular prisms, 8 triangular pyramids.^[1]

Cubic cupola
Schlegel diagram
Type	Polyhedral cupola
Schläfli symbol	{4,3} v rr{4,3}
Cells	28	1 rr{4,3} 1+6 {4,3} 12 {}×{3} 8 {3,3}
Faces	80	32 triangles 48 squares
Edges	84
Vertices	32
Dual
Symmetry group	[4,3,1], order 48
Properties	convex, regular-faced

Related polytopes

The cubic cupola can be sliced off from a runcinated tesseract, on a hyperplane parallel to cubic cell. The cupola can be seen in an edge-centered (B₃) orthogonal projection of the runcinated tesseract:

Runcinated tesseract	Cube (cupola top)	Rhombicuboctahedron (cupola base)
B2 Coxeter plane
B3 Coxeter plane

See also

• Cubic pyramid
• Octahedral cupola
• Runcinated tesseract