Great Dodecahedron Calculator

Calculations at a great dodecahedron. This is the third of four Kepler-Poinsot polyhedra or regular star polyhedra, which are regular, non-convex polyhedra. The great dodecahedron is made from an icosahedron with edge length a, where on each face a regular triangular pyramid is removed, so that pentagonal faces appear.
Enter one value and choose the number of decimal places. Then click Calculate.

	Edge length (a):			12 faces, 60 sides, 30 edges a, 60 ridges s, 12 peaks Faces: 12 regular pentagons Sides: isosceles triangles with legs s and base a
	Ridge length (s):
	Circumsphere radius (rc):
	Pyramid height (hp):
	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.

Length, radius and height have the same unit (e.g. meter), surface areas have 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 four Kepler-Poinsot polyhedra are the small stellated dodecahedron, the great stellated dodecahedron, the great dodecahedron, and the great icosahedron. The great dodecahedron is formed by extending the faces of a dodecahedron until they intersect to form new edges. Star pyramids sit upon the new faces of the dodecahedron. Visually, the great dodecahedron can be thought of as a dodecahedron with twelve star-like points, even though, geometrically, it is not simply created by attaching pyramids. The convex hull of the great dodecahedron is an icosahedron, while a dodecahedron lies within its interior. All three solids share the same center. The dodecahedron visible within the great dodecahedron is smaller than a regular dodecahedron with the same edge length a. The dual polyhedron of the great dodecahedron is the small stellated dodecahedron.
The great dodecahedron, along with the great icosahedron, was discovered in 1809 by the French mathematician and physicist Louis Poinsot. He also recognized that the two star polyhedra previously known and described by Johannes Kepler were likewise regular polyhedra. The great dodecahedron is a rarely encountered shape. While it is sometimes used for decorative purposes, there appear to be no natural occurrences of comparable forms.

Calculation of volume and other dimensions: great dodecahedron

Last updated on 06/13/2026. Author: Jürgen Kummer

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