“Square gyrobicupola”的意思、由来-开放百科全书

词条

Square gyrobicupola

释义

Formulae
Related polyhedra and honeycombs
References
External links

{{Infobox polyhedron
|image=Square gyrobicupola.png
|type=Johnson
J₂₈ - J₂₉ - J₃₀
|faces=8 triangles
2+8 squares
|edges=32
|vertices=16
|symmetry=D_4d
|vertex_config=8(3.4.3.4)
8(3.4³)
|dual=Elongated square trapezohedron
|properties=convex
|net=Johnson solid 29 net.png
}}

In geometry, the square gyrobicupola is one of the Johnson solids (J₂₉). Like the square orthobicupola (J₂₈), it can be obtained by joining two square cupolae (J₄) along their bases. The difference is that in this solid, the two halves are rotated 45 degrees with respect to one another.

The square gyrobicupola is the second in an infinite set of gyrobicupolae.

Related to the square gyrobicupola is the elongated square gyrobicupola. This polyhedron is created when an octagonal prism is inserted between the two halves of the square gyrobicupola. It is argued whether or not the elongated square gyrobicupola is an Archimedean solid because, although it meets every other standard necessary to be an Archimedean solid, it is not highly symmetric.

Formulae

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

Related polyhedra and honeycombs

The square gyrobicupola forms space-filling honeycombs with tetrahedra, cubes and cuboctahedra; and with tetrahedra, square pyramids, and elongated square bipyramids. (The latter unit can be decomposed into elongated square pyramids, cubes, and/or square pyramids).^[2]

References

1. ^Stephen Wolfram, "Triangular gyrobicupola" from Wolfram Alpha. Retrieved July 23, 2010.
2. ^http://woodenpolyhedra.web.fc2.com/J29.html

External links

{{mathworld2 | urlname2 = JohnsonSolid | title2 = Johnson solid| urlname = SquareGyrobicupola | title = Square gyrobicupola }}

1 : Johnson solids

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。