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

词条

Elongated pentagonal gyrocupolarotunda

释义

Formulae
References
External links

{{Infobox polyhedron
|image=elongated_pentagonal_gyrocupolarotunda.png
|type=Johnson
J₄₀ - J₄₁ - J₄₂
|faces=3x5 triangles
3x5 squares
2+5 pentagons
|edges=70
|vertices=35
|symmetry=C_5v
|vertex_config=10(3.4³)
10(3.4².5)
5(3.4.5.4)
2.5(3.5.3.5)
|dual=-
|properties=convex
|net=Johnson solid 41 net.png
}}

In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids (J₄₁). As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda (J₃₃) by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola (J₅) or the pentagonal rotunda (J₆) through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda (J₄₀).

Formulae

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

References

1. ^Stephen Wolfram, "Elongated pentagonal gyrocupolarotunda" from Wolfram Alpha. Retrieved July 25, 2010.

External links

{{Mathworld2 | urlname = ElongatedPentagonalGyrocupolarotunda | title = Elongated pentagonal gyrocupolarotunda | urlname2 = JohnsonSolid | title2 = Johnson solid }}

1 : Johnson solids

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