The Metabiaugmented Truncated Dodecahedron

The metabiaugmented truncated dodecahedron is the 70th Johnson solid, or J70 for short. It has 52 faces (10 decagons, 2 pentagons, 10 squares, and 30 triangles), 120 edges, and 70 vertices. It is obtained by augmenting two non-opposite, non-adjacent decagonal faces of the truncated dodecahedron with pentagonal cupolae (J5).

A metabiaugmented
truncated dodecahedron

If one of the augments is removed, the result is the augmented truncated dodecahedron (J68). A third augment can be added on a decagon non-adjacent to the existing augments, producing the triaugmented truncated dodecahedron (J71).


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

Projection Description

Top view.

Front view.

Diagonal side view.

View centered on decagon.


The Cartesian coordinates of the metabiaugmented 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 12 Mar 2019.

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