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Disphenocingulum

90th Johnson solid (22 faces) From Wikipedia, the free encyclopedia

Disphenocingulum
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In geometry, the disphenocingulum is a Johnson solid with 20 equilateral triangles and 4 squares as its faces.

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3D model of a disphenocingulum

Properties

The disphenocingulum is named by Johnson (1966). The prefix dispheno- refers to two wedgelike complexes, each formed by two adjacent lunesa figure of two equilateral triangles at the opposite sides of a square. The suffix -cingulum, literally 'belt', refers to a band of 12 triangles joining the two wedges.[1] The resulting polyhedron has 20 equilateral triangles and 4 squares, making 24 faces.[2]. All of the faces are regular, categorizing the disphenocingulum as a Johnson solida convex polyhedron in which all of its faces are regular polygonenumerated as 90th Johnson solid .[3]. It is an elementary polyhedron, meaning that it cannot be separated by a plane into two small regular-faced polyhedra.[4]

The surface area of a disphenocingulum with edge length can be determined by adding all of its faces, the area of 20 equilateral triangles and 4 squares , and its volume is .[2]

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Cartesian coordinates

Let be the second smallest positive root of the polynomial and and . Then, the 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.[5]

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References

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