Disphenocingulum | |
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Type |
Johnson J89 – J90 – J91 |
Faces | 20
triangles 4 squares |
Edges | 38 |
Vertices | 16 |
Vertex configuration | 4(32.42) 4(35) 8(34.4) |
Symmetry group | D2d |
Properties | convex |
Net | |
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In geometry, the disphenocingulum is a Johnson solid with 20 equilateral triangles and 4 squares as its faces.
The disphenocingulum is named by Johnson (1966). The prefix dispheno- refers to two wedgelike complexes, each formed by two adjacent lunes—a 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 solid—a convex polyhedron in which all of its faces are regular polygon—enumerated as 90th Johnson solid . [3]. It is elementary, 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]
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]