Elongated square cupola | |
---|---|
Type |
Johnson J18 – J19 – J20 |
Faces | 4
triangles 3x4+1 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 one of the Johnson solids (J19). As the name suggests, it can be constructed by elongating a square cupola (J4) by attaching an octagonal prism to its base. The solid can be seen as a rhombicuboctahedron with its "lid" (another square cupola) removed.
A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966. [1]
The following formulae for volume, surface area and circumradius can be used if all faces are regular, with edge length a: [2]
The dual of the elongated square cupola has 20 faces: 8 isosceles triangles, 4 kites, 8 quadrilaterals.
Dual elongated square cupola | Net of dual |
---|---|
The elongated square cupola forms space-filling
honeycombs with
tetrahedra and
cubes; with cubes and
cuboctahedra; and with tetrahedra,
elongated square pyramids, and
elongated square bipyramids. (The latter two units can be decomposed into cubes and
square pyramids.)
[3]