Gyroelongated pentagonal rotunda | |
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Type | Johnson J24 - J25 - J26 |
Faces | 4x5+10 triangles 1+5 pentagons 1 decagon |
Edges | 65 |
Vertices | 30 |
Vertex configuration | 2.5(3.5.3.5) 2.5(33.10) 10(34.5) |
Symmetry group | C5v |
Dual polyhedron | see above |
Properties | convex |
Net | |
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In geometry, the gyroelongated pentagonal rotunda is one of the Johnson solids (J25). As the name suggests, it can be constructed by gyroelongating a pentagonal rotunda (J6) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal birotunda (J48) with one pentagonal rotunda 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]
With edge length a, the surface area is
and the volume is
The dual of the gyroelongated pentagonal rotunda has 30 faces: 10 pentagons, 10 rhombi, and 10 quadrilaterals.
Dual gyroelongated pentagonal rotunda | Net of dual |
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