The Triaugmented Dodecahedron
The triaugmented dodecahedron (J61) is the 61st among the Johnson solids. It has 23 vertices, 45 edges, and 24 faces (9 pentagons and 15 triangles). It is constructed by augmenting a dodecahedron with 3 pentagonal pyramids on non-adjacent pentagonal faces.
Here are some views of the triaugmented dodecahedron from various angles:
Side view, parallel to pair of opposite pentagons.
Parallel to pentagon opposite an augment.
The Cartesian coordinates of the triaugmented dodecahedron, centered on the origin and with edge length 2, are:
- (0, ±φ2, ±1)
- (±1, 0, ±φ2)
- (±φ2, ±1, 0)
- (±φ, ±φ, ±φ)
- (0, (7+φ)/5, ±(8φ+1)/5)
- ((7+φ)/5, −(8φ+1)/5, 0)
where φ=(1+√5)/2 is the Golden Ratio.