The Metabiaugmented Truncated Dodecahedron

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The metabiaugmented truncated dodecahedron is the 70th Johnson solid, or J70 for short. It has 52 faces (10 decagons, 2 pentagons, 10 squares, and 30 triangles), 120 edges, and 70 vertices. It is obtained by augmenting two non-opposite, non-adjacent decagonal faces of the truncated dodecahedron with pentagonal cupolae (J5).

If one of the augments is removed, the result is the augmented truncated dodecahedron (J68). A third augment can be added on a decagon non-adjacent to the existing augments, producing the triaugmented truncated dodecahedron (J71).

Projections

Here are some views of the metabiaugmented truncated dodecahedron from various angles:

Projection	Description
	Top view.
	Front view.
	Diagonal side view.
	View centered on decagon.

Coordinates

The Cartesian coordinates of the metabiaugmented truncated dodecahedron with edge length 2 are even permutations of coordinate and all changes of sign of:

• (1, 0, 1+3φ)
• (φ², 1, 2φ²)
• (2φ, φ², φ³)

along with:

• (±(13φ+1)/5, ±1, (6φ+12)/5)
• (±(13φ+6)/5, ±φ, (φ+12)/5)
• (±(18φ+1)/5, 0, (φ+7)/5)

where φ=(1+√5)/2 is the Golden Ratio.