Disheptahedron Calculator

Calculations at a regular disheptahedron, also called anticuboctahedron, twisted cuboctahedron, or triangular orthobicupola. This is Johnson solid J₂₇. A disheptahedron has the same faces as a cuboctahedron, except that one half is rotated by 60 degrees. Consequently, both also share the same dimensions.
Enter one value and choose the number of decimal places. Then click Calculate.

	Edge length (a):			14 faces, 24 edges, 12 vertices Faces: 8 equilateral triangles, 6 squares
	Surface area (A):
	Volume (V):
	Circumsphere radius (rc):
	Midsphere radius (rm):
	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.

Edge length and radius have the same 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.

Dishepta is derived from Ancient Greek and means twice seven. Thus, disheptahedron is the name for a 14-faced polyhedron. While the name could technically apply to other shapes, the term disheptahedron usually refers to this specific form. On the other hand, the alternative name triangular orthobicupola references the Johnson solid J₃, the triangular cupola. The disheptahedron consists of two such triangular cupolae joined together as mirror images at their hexagonal bases. The hexagonal base of a cupola thus serves as a plane of symmetry for the triangular bicupola. Consequently, unlike the cuboctahedron, this shape exhibits mirror symmetry to a plane along its edges, though the cuboctahedron remains the more regular form. The disheptahedron possesses three additional planes of symmetry that intersect its edges. Overall, the disheptahedron has fewer planes of symmetry than the cuboctahedron.
The square bicupola is Johnson solid J₂₈, and the pentagonal bicupola is J₃₀.

In chemistry and crystallography, the disheptahedron serves as a model for certain coordination polyhedra. It appears, for instance, in the context of hexagonal close-packing, which describes an ideal hexagonal arrangement of spheres.

Calculation of volume and other dimensions: disheptahedron

Last updated on 06/30/2026. Author: Jürgen Kummer

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