Calculations in a great stellated dodecahedron. This is the second of four Kepler-Poinsot polyhedra or regular star polyhedra, which are regular, non-convex (concave) polyhedra. The great stellated dodecahedron is made from an icosahedron with edge length a, whose edges are extended so that three meet in one point. As a result, a fitting right pyramid with an equilateral triangle as base is attached to each of its faces. The sides of the pyramid are isosceles triangles, the ratio of ridge s to edge a is that of the golden ratio, like in the pentagram b to c. s, c and A are the same as at the small stellated dodecahedron. Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:
s = a/2 * ( 1 + √5 ) = a * φ
c = a * ( 2 + √5 ) = a + 2s
r_{U} = a/4 * √3 * ( 3 + √5 )
h_{p} = a/6 * √3 * ( 3 + √5 )
A = 15a² * √5 + 2√5
V = 5/4a³ * ( 3 + √5 )

Golden ratio phi:
φ = ( 1 + √5 ) / 2 = 1.618033988749895...

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}.