“Elongated pentagonal cupola”的意思、由来-开放百科全书

词条

Elongated pentagonal cupola

释义

Formulas
Dual polyhedron
References
External links

{{Infobox polyhedron
|image=elongated_pentagonal_cupola.png
|type=Johnson
J₁₉ - J₂₀ - J₂₁
|faces=5 triangles
15 squares
1 pentagon
1 decagon
|edges=45
|vertices=25
|symmetry=C_5v|
|vertex_config=10(4².10)
10(3.4³)
5(3.4.5.4)
|dual=-
|properties=convex
|net=Johnson solid 20 net.png
}}

In geometry, the elongated pentagonal cupola is one of the Johnson solids (J₂₀). As the name suggests, it can be constructed by elongating a pentagonal cupola (J₅) by attaching a decagonal prism to its base. The solid can also be seen as an elongated pentagonal orthobicupola (J₃₈) with its "lid" (another pentagonal cupola) removed.

Formulas

The following formulas for the volume and surface area can be used if all faces are regular, with edge length a:^[1]

Dual polyhedron

The dual of the elongated pentagonal cupola has 25 faces: 10 isosceles triangles, 5 kites, and 10 quadrilaterals.

Dual elongated pentagonal cupola	Net of dual

References

1. ^Stephen Wolfram, "Elongated pentagonal cupola" from Wolfram Alpha. Retrieved July 22, 2010.

External links

{{mathworld2 | urlname2 = JohnsonSolid | title2 = Johnson solid| urlname =ElongatedPentagonalCupola| title = Elongated pentagonal cupola}}

1 : Johnson solids

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