The Augmented Dodecahedron

The augmented dodecahedron (J58) is the 58th Johnson solid. It has 21 vertices, 35 edges, and 16 faces (11 pentagons and 5 triangles). It can be constructed augmenting a dodecahedron with a pentagonal pyramid.

An augmented

Adding a second pentagonal pyramid on the opposite side produces the parabiaugmented dodecahedron (J59). Adding the second pyramid to a face one edge away from the first pyramid produces instead the metabiaugmented dodecahedron (J60).


Here are some views of the augmented dodecahedron from various angles:

Projection Description

Top view.

Side view.

Front view.


The Cartesian coordinates of the augmented dodecahedron, centered on the origin and with edge length 2, are:

where φ=(1+√5)/2 is the Golden Ratio.

Last updated 10 Jan 2019.

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