“Trigyrate rhombicosidodecahedron”的意思、由来-开放百科全书

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Trigyrate rhombicosidodecahedron

释义

References
External links

{{Infobox polyhedron
|image=trigyrate_rhombicosidodecahedron.png
|type=Johnson
J₇₄ - J₇₅ - J₇₆
|faces=2+2x3+2x6 triangles
4x3+3.6 squares
4x3 pentagons
|edges=120
|vertices=60
|symmetry=C_3v
|vertex_config=5x6(3.4².5)
4x3+3x6(3.4.5.4)
|dual=-
|properties=convex
|net=Johnson solid 75 net.png
}}

In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (J₇₅). It contains 20 triangles, 30 squares and 12 pentagons.

It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae rotated through 36 degrees.

Related Johnson solids are

the gyrate rhombicosidodecahedron (J₇₂) where one cupola is rotated,

the parabigyrate rhombicosidodecahedron (J₇₃) where two opposing cupolae are rotated and

the metabigyrate rhombicosidodecahedron (J₇₄) where two non-opposing cupolae are rotated.

References

Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
{{cite book|author=Victor A. Zalgaller|title=Convex Polyhedra with Regular Faces|publisher=Consultants Bureau|year=1969|id=No ISBN}} The first proof that there are only 92 Johnson solids.

External links

{{Mathworld2 | urlname2 = JohnsonSolid | title2 = Johnson solid | urlname =TrigyrateRhombicosidodecahedron | title = Trigyrate rhombicosidodecahedron }}

1 : Johnson solids

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