Elongated pentagonal gyrobirotunda

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Elongated pentagonal gyrobirotunda
Elongated pentagonal gyrobirotunda.png
Type Johnson
J42 – J43 – J44
Faces 10+10 triangles
10 squares
2+10 pentagons
Edges 80
Vertices 40
Vertex configuration 20(3.42.5)
2.10(3.5.3.5)
Symmetry group D5d
Dual polyhedron -
Properties convex
Net
Johnson solid 43 net.png

In geometry, the elongated pentagonal gyrobirotunda or elongated icosidodecahedron is one of the Johnson solids (J43). As the name suggests, it can be constructed by elongating a "pentagonal gyrobirotunda," or icosidodecahedron (one of the Archimedean solids), by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal rotundae (J6) through 36 degrees before inserting the prism yields an elongated pentagonal orthobirotunda (J42).

Contents

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]

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a: [2]

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

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<span class="mw-page-title-main">Elongated pentagonal orthobirotunda</span> 42nd Johnson solid

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<span class="mw-page-title-main">Elongated pentagonal cupola</span> 20th Johnson solid

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<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">Pentagonal gyrobicupola</span> 31st Johnson solid; 2 pentagonal cupolae joined base-to-base

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<span class="mw-page-title-main">Elongated pentagonal orthobicupola</span> 38th Johnson solid

In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal orthobicupola by inserting a decagonal prism between its two congruent halves. Rotating one of the cupolae through 36 degrees before inserting the prism yields an elongated pentagonal gyrobicupola.

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<span class="mw-page-title-main">Elongated triangular cupola</span> 18th Johnson solid

In geometry, the elongated triangular cupola is one of the Johnson solids. As the name suggests, it can be constructed by elongating a triangular cupola by attaching a hexagonal prism to its base.

<span class="mw-page-title-main">Pentagonal orthocupolarotunda</span> 32nd Johnson solid; pentagonal cupola and rotunda joined base-to-base

In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids. As the name suggests, it can be constructed by joining a pentagonal cupola and a pentagonal rotunda along their decagonal bases, matching the pentagonal faces. A 36-degree rotation of one of the halves before the joining yields a pentagonal gyrocupolarotunda.

<span class="mw-page-title-main">Elongated triangular gyrobicupola</span> 36th Johnson solid

In geometry, the elongated triangular gyrobicupola is one of the Johnson solids. As the name suggests, it can be constructed by elongating a "triangular gyrobicupola," or cuboctahedron, by inserting a hexagonal prism between its two halves, which are congruent triangular cupolae. Rotating one of the cupolae through 60 degrees before the elongation yields the triangular orthobicupola.

<span class="mw-page-title-main">Elongated pentagonal gyrocupolarotunda</span> 41st Johnson solid

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

<span class="mw-page-title-main">Elongated pentagonal orthocupolarotunda</span> 40th Johnson solid

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

References

  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 .
  2. ↑ Stephen Wolfram, "Elongated pentagonal gyrobirotunda" from Wolfram Alpha. Retrieved July 26, 2010.
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