Truncated Icosidodecahedron Calculator

Name: Truncated Icosidodecahedron - Geometry Calculator
Author: Jürgen Kummer

Calculations at a regular truncated icosidodecahedron. This shape is also known as great rhombicosidodecahedron, see also the small rhombicosidodecahedron. A truncated icosidodecahedron is constructed by cutting off the vertices of an icosidodecahedron in a way, so that every edge has the same length. Its dual body is the hexakis icosahedron.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

A = 30 a^{2} \cdot (1 + \sqrt{3} + \sqrt{5 + 2 \sqrt{5}})

V = 5 a^{3} \cdot (19 + 10 \sqrt{5})

r_{c} = \frac{a}{2} \cdot \sqrt{31 + 12 \sqrt{5}}

r_{m} = \frac{a}{2} \cdot \sqrt{30 + 12 \sqrt{5}}

The truncated icosidodecahedron is an Archimedean solid. Edge length and radius 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.

The truncated icosidodecahedron is one of three Archimedean solids composed of three different types of faces. The other two are the truncated cuboctahedron and the rhombicosidodecahedron. Together with the truncated dodecahedron, the truncated icosidodecahedron features the polygons with the highest number of vertices among the Archimedean solids, decagons. In the truncated icosidodecahedron, the vertices sliced off from the icosidodecahedron become squares. The equilateral triangles and regular pentagons effectively double their vertex count through this truncation process, thereby transforming into hexagons and decagons, respectively.

The truncated icosidodecahedron is one of the most complex Archimedean solids. Due to its high number of faces, 62, it closely approximates a sphere. This shows in the fact that its circumsphere radius and its midsphere radius lie very close to one another. It is rarely encountered in the real world, though it may occasionally find application in architecture and design. Thanks to its uniformity and high degree of symmetry, it appears more harmonious than other large Archimedean solids, such as the snub dodecahedron. It could, for instance, serve as a lampshade, though it would be more difficult to manufacture than simpler solids.

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