Gyroelongated pentagonal rotunda

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Gyroelongated pentagonal rotunda
Gyroelongated pentagonal rotunda.png
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
Johnson solid 25 net.png

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.

Contents

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]

Area and Volume

With edge length a, the surface area is

and the volume is

Dual polyhedron

The dual of the gyroelongated pentagonal rotunda has 30 faces: 10 pentagons, 10 rhombi, and 10 quadrilaterals.

Dual gyroelongated pentagonal rotundaNet of dual
Dual gyroelongated pentagonal rotunda.png Dual gyroelongated pentagonal rotunda net.png
  1. Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics , 18: 169–200, doi:10.4153/cjm-1966-021-8, MR   0185507, Zbl   0132.14603 .