Elongated pentagonal pyramid explained

Type:	Johnson
Faces:	5 triangles 5 squares 1 pentagon
Edges:	20
Vertices:	11
Dual:	self
Properties:	convex
Net:	Elongated_Pentagonal_Pyramid_Net.svg

In geometry, the elongated pentagonal pyramid is one of the Johnson solids . As the name suggests, it can be constructed by elongating a pentagonal pyramid by attaching a pentagonal prism to its base.

Formulae

The following formulae for the height (

H ), surface area (A ) and volume (V ) can be used if all faces are regular, with edge length L :^[1] H = L ⋅ \left( 1 + \sqrt{ (5- \sqrt{ 5)/() }}\right) \approx L\cdot 1.525731112A = L ^{2} ⋅ (20+5 \sqrt{ 3)/(+) \sqrt{ 25 + 10 \sqrt{ 5 }}}{ 4 } ≈ L ^{2 ⋅} 8 . 88554091 V = L ^{3} ⋅ \left( (5+ \sqrt{ 5)/(+) 6 \sqrt{ 25 + 10 \sqrt{ 5 }}}{ 24 } \right) ≈ L ^{3 ⋅} 2 . 021980233

Dual polyhedron

The dual of the elongated pentagonal pyramid has 11 faces: 5 triangular, 1 pentagonal and 5 trapezoidal. It is topologically identical to the Johnson solid.

See also

• Elongated pentagonal bipyramid

Notes and References

1. Sapiña . R. . Area and volume of the Johnson solid J₉ . 2659-9899 . 2020-08-30 . es . Problemas y ecuaciones.