Deltoidal Hexecontahedron Calculator

Calculations at a deltoidal hexecontahedron, the dual body of the rhombicosidodecahedron. A deltoidal hexecontahedron is a polyhedron with deltoid (kite) faces, those have two angles with 86.97°, one angle with 118.3° and one with 67.8°. It has twenty vertices with three edges, thirty vertices with four edges and twelve vertices with five edges.
Enter one value and choose the number of decimal places. Then click Calculate.

	Long edge (a):			60 faces, 120 edges, 62 vertices Faces: kites (deltoids) One of the deltoid faces.
	Short edge (b):
	Symmetry diagonal (e):
	Other diagonal (f):
	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 * 3/22 * ( 7 - √5 ) e = 3a * √ ( 5 - √5 ) / 20 f = a/11 * √ ( 470 + 156√5 ) / 5 A = 9/11 * a² * √ 10 * ( 157 + 31√5 ) V = 45/11 * a³ * √ ( 370 + 164√5 ) / 25 rm = 3/20 * a * ( 5 + 3√5 ) ri = 3/2 * a * √ ( 135 + 59√5 ) / 205

A/V = 9/45 * √ 10 * ( 157 + 31√5 ) / ( a * √ ( 370 + 164√5 ) / 25 )

The deltoidal hexecontahedron is a Catalan solid. Edge lengths, diagonals and radiuses 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.