Disphenocingulum Calculator

Calculations at a disphenocingulum, the Johnson solid J₉₀. This is a polyhedron of 20 equilateral triangles and 4 squares.
Enter one value and choose the number of decimal places. Then click Calculate.

	Edge length (a):			24 faces, 38 edges, 16 vertices
	Surface area (A):
	Volume (V):
	Surface-to-volume ratio (A/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

The length has an one-dimensional unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The term disphenocingulum is derived from Ancient Greek and Latin and translates to double-wedge belt. The two pairs of squares, surrounded by a belt of equilateral triangles, are interpreted as the wedges. It is the third-to-last of the 92 Johnson solids and is an elementary polyhedron, meaning it cannot be assembled from two or more regular polyhedra.

The two wedges of the disphenocingulum are positioned opposite each other but are rotated by 90 degrees. The edges between the pairs of squares are orthogonal and skew. That is, they appear perpendicular to one another when projected onto a plane parallel to those edges. The disphenocingulum has four vertices where four edges meet, these are the vertices where two squares touch. The other twelve vertices have five incident edges. At four of these vertices, five triangles meet, while at the remaining eight, four triangles and one square meet. Thus, there are three distinct types of vertices in this shape. The sharpest vertices are those where the five equilateral triangles meet.
The disphenocingulum possesses neither reflectional nor point symmetry, nor does it have any non-trivial rotational symmetry. For a polyhedron composed of regular polygons, it presents a highly irregular and confusing appearance.

Unlike its surface area, there is no simple, exact formula for the volume of the disphenocingulum. Calculation relies on vertex coordinates that cannot be expressed using radical expressions. Consequently, the volume is typically stated only as a numerical approximation.

Calculation of volume and other dimensions: disphenocingulum

Last updated on 07/12/2026. Author: Jürgen Kummer

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