The Truncated Dodecahedron
The truncated dodecahedron is a 3D uniform polyhedron bounded by 20 triangles and 12 decagons. It may be constructed by truncating the dodecahedron's vertices such that its pentagonal faces become decagons. Alternatively, it may be constructed by radially expanding the edges of the dodecahedron outwards, thus turning vertices into triangles and pentagons into decagons.
Projections
In order to be able to identify the truncated dodecahedron in various projections of 4D objects, it is useful to know how it appears from various viewpoints. The following are some of the commonlyencountered views:
Projection  Envelope  Description 

Dodecagon  Parallel projection centered on a decagonal face. 

Icositetragon  Parallel projection centered on a triangular face. 

Nonuniform decagon  Parallel projection centered on an edge shared between two decagons. 

Icositetragon  Vertexcentered parallel projection. 
Coordinates
The Cartesian coordinates of the truncated dodecahedron, centered on the origin and having edge length 2, are all even permutations of coordinates and changes of sign of:
 (0, 1, 1+3φ)
 (1, φ^{2}, 2φ^{2})
 (φ^{2}, 2φ, φ^{3})
where φ=(1+√5)/2 is the Golden Ratio.
Occurrences
The truncated dodecahedron occurs as cells in the following uniform polychora:
 The truncated 120cell;
 The runcitruncated 120cell.