Calculations at a regular truncated dodecahedron. A truncated dodecahedron is constructed by cutting off the vertices of an dodecahedron in a way, so that every edge after truncating has the same length again. Its dual body is the triakis icosahedron. Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
The truncated dodecahedron 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 dodecahedron has 32 faces, 90 edges, and 60 vertices. The faces consist of 20 equilateral triangles and 12 regular decagons. At each vertex of the original dodecahedron, there are three regular pentagons. Therefore, when a vertex is regularly truncated, an equilateral triangle is formed there. Each of the dodecahedron's pentagons has one vertex removed and two new ones added, thus doubling the number of vertices on these faces. The pentagons become decagons, with the newly formed triangles positioned between them. At each vertex of the truncated dodecahedron, there are two regular decagons and one equilateral triangle.
The truncated dodecahedron is far less well-known and occurs much less frequently in real-world objects than the next Archimedean solid, the truncated icosahedron. It appears in some theoretical molecular models and is occasionally used in part for design and experimental architecture, for example, for dome-like structures. However, its decagons are quite large, resulting in extensive flat surfaces, which limits its use where more spherical shapes are required.
In Euclidean space, the regular truncated dodecahedron is not a space-filling polyhedron. Even together with other known regular or uniform polyhedra, it does not form a known gapless space-filling structure. Corresponding honeycombs with truncated dodecahedra are so far only known in non-Euclidean geometries.