Edges 45 Symmetry group C5v | Vertices 25 | |
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Type JohnsonJ19 - J20 - J21 Vertex configuration 10(4.10)10(3.4)5(3.4.5.4) | ||
In geometry, the elongated pentagonal cupola is one of the Johnson solids (J20). As the name suggests, it can be constructed by elongating a pentagonal cupola (J5) by attaching a decagonal prism to its base. The solid can also be seen as an elongated pentagonal orthobicupola (J38) with its "lid" (another pentagonal cupola) removed.
Contents
A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (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.
Formulas
The following formulas for the volume and surface area can be used if all faces are regular, with edge length a:
Dual polyhedron
The dual of the elongated pentagonal cupola has 25 faces: 10 isosceles triangles, 5 kites, and 10 quadrilaterals.