The Biaugmented Truncated Cube
The biaugmented truncated cube is the 67th Johnson solid, or J67 for short. It is bounded by 16 equilateral triangles, 10 squares, and 4 regular octagons, for a total of 30 faces, 60 edges, and 32 vertices. It is constructed by augmenting a truncated cube with two square cupolae (J4) on opposite sides.
If one square cupola is removed, the result is the augmented truncated cube (J66).
Projections
Here are some views of the biaugmented truncated cube from various angles:
| Projection | Description |
|---|---|
 |
Top view. |
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Front view. |
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Diagonal side view. |
Coordinates
The Cartesian coordinates of the biaugmented 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))
