Trigyrate rhombicosidodecahedron
- Trigyrate rhombicosidodecahedron
Infobox_Polyhedron with net
Polyhedron_Type=Johnson
J74 - J75 - J76
Face_List=2+2x3+2x6 triangles
4x3+3.6 squares
4x3 pentagons
Edge_Count=120
Vertex_Count=60
Symmetry_Group="C"3v
Vertex_List=5x6(3.42.5)
4x3+3x6(3.4.5.4)
Dual=-
Property_List=convex
Net_
In geometry, the Trigyrate rhombicosidodecahedron is one of the
Johnson solids ("J"75).It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae rotated through 36 degrees.Related Johnson solids are the gyrate rhombicosidodecahedron ("J"72) where one cupola is rotated,the parabigyrate rhombicosidodecahedron ("J"73) where two opposing cupolae are rotated and the metabigyrate rhombicosidodecahedron ("J"74) where two non-opposing cupolae are rotated.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
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
*
** MathWorld | urlname=TrigyrateRhombicosidodecahedron | title=Trigyrate rhombicosidodecahedron
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