The Parabiaugmented Truncated Dodecahedron

The parabiaugmented truncated dodecahedron is the 69th Johnson solid, or J69 for short. It has 52 faces (10 decagons, 2 pentagon, 10 squares, and 30 triangles), 120 edges, and 70 vertices. It is obtained by augmenting two opposite decagonal faces of the truncated dodecahedron with pentagonal cupolae (J5).

A parabiaugmented
truncated dodecahedron

If one of the augments is removed, the result is the augmented truncated dodecahedron (J68).


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

Projection Description

Top view.

Front view.

Diagonal side view.

Oblique view centered on decagon-decagon edge.

Oblique view centered on decagon-triangle edge.


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

along with:

where φ=(1+√5)/2 is the Golden Ratio.

Last updated 18 Jun 2019.

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