The Augmented Truncated Dodecahedron

The augmented truncated dodecahedron is the 68th Johnson solid, or J68 for short. It has 42 faces (11 decagons, 1 pentagon, 5 squares, and 25 triangles), 105 edges, and 65 vertices. It is constructed by augmenting a truncated dodecahedron with a pentagonal cupola (J5).

An augmented truncated

Adding a second augment on the opposite decagon produces the parabiaugmented truncated dodecahedron (J69). Placing the second augment on a non-adjacent decagon that isn't the opposite one produces the metabiaugmented truncated dodecahedron (J70). The latter can take a third augment, producing the triaugmented truncated dodecahedron (J71).


Here are some views of the augmented truncated dodecahedron from various angles:

Projection Description

Top view.

Front view.

Diagonal side view.

Oblique view centered on decagon-decagon edge.

Oblique view centered on decagon-triangle edge.


The Cartesian coordinates of the augmented truncated dodecahedron with edge length 2 are even permutations of coordinate and all changes of sign of:

along with:

where φ=(1+√5)/2 is the Golden Ratio.

Last updated 18 Jun 2019.

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