Sphenocorona Calculator

Calculations at a sphenocorona, the Johnson solid J₈₆. This is a polyhedron of ten equilateral triangles and two squares.
Enter one value and choose the number of decimal places. Then click Calculate.

	Edge length (a):			12 faces, 22 edges, 10 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 name sphenocorona is derived from Ancient Greek and means wedge wreath or wedge crown. The idea here is that the two squares form a wedge, while the triangles are arranged in a wreath-like manner around it.

The sphenocorona is an elementary or non-composite polyhedron, as it cannot be assembled from two or more other regular polyhedra. Most other Johnson solids are composite polyhedra. This characteristic is the reason the sphenocorona has been included here. The next Johnson solid, J₈₇, is the augmented sphenocorona, formed by attaching a square pyramid (Johnson solid J₁) to one of the sphenocorona's squares. If a second such pyramid is attached to the other square, the result is a non-convex polyhedron.
The sphenocorona exhibits reflectional symmetry across two planes. One plane runs along the line where the two squares meet, bisecting the two opposite triangles. The other plane of symmetry passes through the midpoints of the three parallel edges of the squares, of which the middle one lies on the first plane of symmetry. These two planes are perpendicular to each other. Additionally, the sphenocorona possesses rotational symmetry for rotations of 180 degrees and multiples thereof about an axis extending from the midpoint of the edge shared by the two squares to the midpoint of the edge shared by the two opposite triangles. In the sketch above, this corresponds to a 180-degree rotation of the image.

Last updated on 07/09/2026. Author: Jürgen Kummer

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