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Rhombic Triacontahedron Calculator

Calculations at a rhombic triacontahedron, the dual body of the icosidodecahedron. A rhombic triacontahedron is a polyhedron with rhombic faces, those have angles of 63.435° and 116.565°. It has twenty vertices with three edges and twelve vertices with five edges.
Enter one value and choose the number of decimal places. Then click Calculate.


Eugène Charles Catalan, by Emile Delperée Edge length (a): Rhombic Triacontahedron
30 faces, 60 edges, 32 vertices
Faces: rhombi
Surface area (A):
Volume (V):
Midsphere radius (rm):
Insphere radius (ri):
Surface-to-volume ratio (A/V):
Round to    decimal places.



Formulas:
A = 12 * a² * √5
V = 4 * a³ * √ 5 + 2√5
rm = a/5 * ( 5 + √5 )
ri = a * √ ( 5 + 2√5 ) / 5
A/V = 3 * √5 / ( √ 5 + 2√5 * a )

The rhombic triacontahedron is a Catalan solid. Edge length 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.



Last updated on 07/10/2025.

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Cite this page: Rechneronline (2025) - Rhombic Triacontahedron.
Retrieved on 2026-04-22 from https://rechneronline.de/pi/rhombic-triacontahedron.php




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