Calculations in a small stellated dodecahedron. This is the first of four Kepler-Poinsot polyhedra or regular star polyhedra, which are regular, non-convex (concave) polyhedra. The small stellated dodecahedron is made from a dodecahedron with edge length a, whose edges are extended so that five meet in one point. As a result, a fitting right pyramid with a regular pentagon 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 great stellated dodecahedron. Enter one value and choose the number of decimal places. Then click Calculate.

Edge a, ridge s and face P.

Formulas:
s = a/2 * ( 1 + √5 ) = a * φ
c = a * ( 2 + √5 ) = a + 2s
r_{c} = a/4 * √50 + 22√5
h_{p} = a/5 * √25 + 10√5
A = 15a² * √5 + 2√5
V = 5/4a³ * ( 7 + 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}.