The Augmented Dodecahedron

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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.

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).

Projections

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

Projection	Description
	Top view.
	Side view.
	Front view.

Coordinates

The Cartesian coordinates of the augmented 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)

where φ=(1+√5)/2 is the Golden Ratio.