Edges 55 Symmetry group C5v | Vertices 30 | |
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Type JohnsonJ20 - J21 - J22 Faces 2.5 triangles2.5 squares1+5 pentagons1 decagon Vertex configuration 10(4.10)10(3.4.5)2.5(3.5.3.5) | ||
In geometry, the elongated pentagonal rotunda is one of the Johnson solids (J21). As the name suggests, it can be constructed by elongating a pentagonal rotunda (J6) by attaching a decagonal prism to its base. It can also be seen as an elongated pentagonal orthobirotunda (J42) with one pentagonal rotunda removed.
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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.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:
Dual polyhedron
The dual of the elongated pentagonal rotunda has 30 faces: 10 isosceles triangles, 10 rhombi, and 10 quadrilaterals.