Elongated square cupola
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| Elongated square cupola | |
|---|---|
 | |
| Type | Johnson J18 – J19 – J20 |
| Faces | 4 triangles 13 squares 1 octagon |
| Edges | 36 |
| Vertices | 20 |
| Vertex configuration | 8(42.8) 4+8(3.43) |
| Symmetry group | C4v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
In geometry, the elongated square cupola is a polyhedron constructed from an octagonal prism by attaching square cupola onto its base. It is an example of Johnson solid.
The elongated square cupola is constructed from an octagonal prism by attaching a square cupola onto one of its bases, a process known as the elongation.[1] This cupola covers the octagonal face so that the resulting polyhedron has four equilateral triangles, thirteen squares, and one regular octagon.[2] It can also be constructed by removing a square cupola from a rhombicuboctahedron, which would also make it a diminished rhombicuboctahedron. A convex polyhedron in which all of the faces are regular polygons is the Johnson solid. The elongated square cupola is one of them, enumerated as the nineteenth Johnson solid .[3]
