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

Properties

The disphenocingulum is named by. 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. The resulting polyhedron has 20 equilateral triangles and 4 squares, making 24 faces.. 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 J_{90}.. It is an elementary polyhedron, meaning that it cannot be separated by a plane into two small regular-faced polyhedra. The surface area of a disphenocingulum with edge length a can be determined by adding all of its faces, the area of 20 equilateral triangles and 4 squares, and its volume is 3.7776a^3.

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.