Supriya Ghosh (Editor)

Gyroelongated pentagonal cupola

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Edges
  
55

Symmetry group
  
C5v

Vertices
  
25

Gyroelongated pentagonal cupola

Type
  
Johnson J23 - J24 - J25

Faces
  
3.5+10 triangles 5 squares 1 pentagon 1 decagon

Vertex configuration
  
5(3.4.5.4) 2.5(3.10) 10(3.4)

In geometry, the gyroelongated pentagonal cupola is one of the Johnson solids (J24). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola (J5) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal bicupola (J46) with one pentagonal cupola removed.

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.

Dual polyhedron

The dual of the gyroelongated pentagonal cupola has 25 faces: 10 kites, 5 rhombi, and 10 quadrilaterals.

References

Gyroelongated pentagonal cupola Wikipedia