Tridiminished rhombicosidodecahedron

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Tridiminished rhombicosidodecahedron
Tridiminished rhombicosidodecahedron.png
Type Johnson
J82 – J83 – J84
Faces 2+3 triangles
3×3+6 squares
3×3 pentagons
3 decagons
Edges 75
Vertices 45
Vertex configuration 5×6(4.5.10)
3×3+6(3.4.5.4)
Symmetry group C3v
Dual polyhedron -
Properties Convex
Net
Johnson solid 83 net.png

In geometry, the tridiminished rhombicosidodecahedron is one of the Johnson solids (J83). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed.

A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids , Archimedean solids , prisms , or antiprisms ). They were named by Norman Johnson , who first listed these polyhedra in 1966. [1]

Related Johnson solids are:

  1. ↑ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics , 18: 169–200, doi:10.4153/cjm-1966-021-8, MR   0185507, Zbl   0132.14603 .

Related Research Articles

In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a strictly convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two solids with such a property: the first solids are the pyramids, cupolas. and a rotunda; some of the solids may be constructed by attaching with those previous solids, whereas others may not. These solids are named after mathematicians Norman Johnson and Victor Zalgaller.

<span class="mw-page-title-main">Rhombicosidodecahedron</span> Archimedean solid

In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.

<span class="mw-page-title-main">Square orthobicupola</span> 28th Johnson solid; 2 square cupolae joined base-to-base

In geometry, the square orthobicupola is one of the Johnson solids. As the name suggests, it can be constructed by joining two square cupolae along their octagonal bases, matching like faces. A 45-degree rotation of one cupola before the joining yields a square gyrobicupola.

<span class="mw-page-title-main">Gyroelongated square bicupola</span> 45th Johnson solid

In geometry, the gyroelongated square bicupola is the Johnson solid constructed by attaching two square cupolae on each base of octagonal antiprism. It has the property of chirality.

<span class="mw-page-title-main">Pentagonal cupola</span> 5th Johnson solid (12 faces)

In geometry, the pentagonal cupola is one of the Johnson solids. It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.

<span class="mw-page-title-main">Diminished rhombicosidodecahedron</span> 76th Johnson solid

In geometry, the diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.

<span class="mw-page-title-main">Gyrate rhombicosidodecahedron</span> 72nd Johnson solid

In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids. It is also a canonical polyhedron.

<span class="mw-page-title-main">Parabidiminished rhombicosidodecahedron</span> 80th Johnson solid

In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids. It is also a canonical polyhedron.

<span class="mw-page-title-main">Metabidiminished rhombicosidodecahedron</span> 81st Johnson solid

In geometry, the metabidiminished rhombicosidodecahedron is one of the Johnson solids.

<span class="mw-page-title-main">Trigyrate rhombicosidodecahedron</span> 75th Johnson solid

In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids. It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron.

<span class="mw-page-title-main">Pentagonal orthobicupola</span> 30th Johnson solid; 2 pentagonal cupolae joined base-to-base

In geometry, the pentagonal orthobicupola is one of the Johnson solids. As the name suggests, it can be constructed by joining two pentagonal cupolae along their decagonal bases, matching like faces. A 36-degree rotation of one cupola before the joining yields a pentagonal gyrobicupola.

<span class="mw-page-title-main">Parabigyrate rhombicosidodecahedron</span> 73rd Johnson solid

In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.

<span class="mw-page-title-main">Paragyrate diminished rhombicosidodecahedron</span> 77th Johnson solid

In geometry, the paragyrate diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and the opposing pentagonal cupola removed.

<span class="mw-page-title-main">Metagyrate diminished rhombicosidodecahedron</span> 78th Johnson solid

In geometry, the metagyrate diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and a non-opposing pentagonal cupola removed.

<span class="mw-page-title-main">Bigyrate diminished rhombicosidodecahedron</span> 79th Johnson solid

In geometry, the bigyrate diminished rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with two pentagonal cupolae rotated through 36 degrees, and a third pentagonal cupola removed.

<span class="mw-page-title-main">Gyrate bidiminished rhombicosidodecahedron</span> 82nd Johnson solid

In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids.

<span class="mw-page-title-main">Metabigyrate rhombicosidodecahedron</span> 74th Johnson solid

In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids. It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.

<span class="mw-page-title-main">Gyroelongated triangular cupola</span>

In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "gyroelongation", which means that an antiprism is joined to the base of a solid, or between the bases of more than one solid.

<span class="mw-page-title-main">Elongated cupola</span>

In geometry, the elongated cupolae are an infinite set of polyhedra, constructed by adjoining an n-gonal cupola to an 2n-gonal prism.

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