The Augmented Tridiminished Icosahedron
The augmented tridiminished icosahedron is the 64th Johnson solid, or J64 for short. It is bounded by 7 triangles and 3 pentagons, for a total of 10 faces, 18 edges, and 10 vertices. It is constructed by augmenting a tridiminished icosahedron (J63) with a tetrahedron (as a triangular pyramid).
Due to the non-equivalence of its vertices, the augmented tridiminished icosahedron only has a single axis of symmetry: a 3-fold symmetry around the line passing through its apex and and the bottom triangle.
Here are some views of the augmented tridiminished icosahedron from various angles:
The Cartesian coordinates of the augmented tridiminished icosahedron are:
- (0, 0, 2(√2+φ)/√3)
- (±1, −1/√3, 2φ/√3)
- ( 0, 2/√3, 2φ/√3)
- (±φ, −φ/√3, 0)
- ( 0, 2φ/√3, 0)
- (±1, 1/√3, −2/√3)
- ( 0, −2/√3, −2/√3)
where φ=(1+√5)/2 is the Golden Ratio.