The Augmented Truncated Cube

The augmented truncated cube is the 66th Johnson solid, or J66 for short. It is bounded by 12 equilateral triangles, 5 squares, and 5 regular octagons, for a total of 22 faces, 48 edges, and 28 vertices. It is constructed by augmenting a truncated cube with a square cupola.

An augmented truncated

A second square cupola can be added on the opposite side, producing the biaugmented truncated cube (J67).


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

Projection Description

Top view.

Front view.

Diagonal side view.


The Cartesian coordinates of the augmented truncated cube are:

Last updated 18 Jun 2019.

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