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.
A second square cupola can be added on the opposite side, producing the biaugmented truncated cube (J67).
Projections
Here are some views of the augmented truncated cube from various angles:
| Projection | Description |
|---|---|
 |
Top view. |
 |
Front view. |
 |
Diagonal side view. |
Coordinates
The Cartesian coordinates of the augmented truncated cube are:
- (±1, ±(1+√2), ±(1+√2))
- (±(1+√2), ±1, ±(1+√2))
- (±(1+√2), ±(1+√2), ±1)
- (0, ±√2, 1+2√2)
- (±√2, 0, 1+2√2)
