Pentagonal Icositetrahedron Calculator

Calculations at a pentagonal icositetrahedron, the dual body of the snub cube. Its faces are axial-symmetric pentagons with the top angle acos(2-t)=80.7517°, base and middle sides b and top sides a. Of this polyhedron, there are two forms which are mirror images of each other, but otherwise identical.
Enter one value and choose the number of decimal places. Then click Calculate.

	Long edge (a):			Left pentagonal icositetrahedron Right pentagonal icositetrahedron 24 faces, 60 edges, 38 vertices
	Short edge (b):
	Snub cube edge (d):
	Surface area (A):
	Volume (V):
	Midsphere radius (rm):
	Insphere radius (ri):
	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.
	Formulas: b = a / (s+1) d = 2a / √ 2 + 2s A = 24a² * ( 2 + 3s ) / ( 1 + 2s ) * √ ( 1 - s ) / ( 1 + s ) V = 4a³ * ( 2 + 3s ) * √ 1 - 2s / [ ( 1 + s ) * ( 1 - 4s² ) ] rm = a / √ 2 * ( 1 + s ) * ( 1 - 2s ) ri = a / ( 2 * √ ( 1 - 2s ) * ( 1 - s² ) )

Tribonacci constant t = ( 1 + ³√ 19 + 3√33 + ³√ 19 - 3√33 ) / 3 = 1.839286755214161...
s = ( t - 1 ) / 2 = 0.41964337760708