Disphenocingulum

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Disphenocingulum
Disphenocingulum.png
Type Johnson
J89 - J90 - J91
Faces 4+2x8 triangles
4 squares
Edges 38
Vertices 16
Vertex configuration 4(32.42)
4(35)
8(34.4)
Symmetry group D2d
Dual polyhedron Order-5 truncated snub disphenoid
Properties convex
Net
Johnson solid 90 net.png
3D model of a disphenocingulum J90 disphenocingulum.stl
3D model of a disphenocingulum

In geometry, the disphenocingulum or pentakis elongated gyrobifastigium is one of the Johnson solids (J90). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.

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]

Cartesian coordinates

Let a ≈ 0.76713 be the second smallest positive root of the polynomial

and and .

Then, Cartesian coordinates of a disphenocingulum with edge length 2 are given by the union of the orbits of the points

under the action of the group generated by reflections about the xz-plane and the yz-plane. [2]

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In geometry, the elongated triangular orthobicupola or cantellated triangular prism is one of the Johnson solids (J35). As the name suggests, it can be constructed by elongating a triangular orthobicupola (J27) by inserting a hexagonal prism between its two halves. The resulting solid is superficially similar to the rhombicuboctahedron, with the difference that it has threefold rotational symmetry about its axis instead of fourfold symmetry.

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. ↑ Timofeenko, A. V. (2009-10-17). "The non-platonic and non-Archimedean noncomposite polyhedra". Journal of Mathematical Sciences. 162 (5): 710–729. doi:10.1007/s10958-009-9655-0. ISSN   1072-3374. S2CID   120114341.
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