The Decagonal Antiprism


The decagonal antiprism is a 3D uniform polyhedron bounded by 2 decagons and 20 triangles. It has 40 edges and 20 vertices.

The decagonal
antiprism

The height of a decagonal antiprism with an edge length of 2 is:

2√(√(11φ+7)−2φ−1)

or approximately 1.724794, where φ=(1+√5)/2 is the Golden Ratio.

A decagonal antiprism can be attached to a pentagonal cupola (J5) to make a gyro­elongated pentagonal cupola (J24), or attached to a pentagonal rotunda (J6) to make a gyro­elongated pentagonal rotunda (J25).

Inserting a decagonal antiprism between two pentagonal cupolae produces the gyro­elongated pentagonal bicupola (J46). Doing so between a pentagonal cupola and a pentagonal rotunda produces the gyro­elongated penta­gonal cupolarotunda (J47); and doing so between two pentagonal rotundae produces the gyro­elongated pentagonal birotunda (J48).

Projections

Here are some views of the decagonal antiprism from various angles:

Projection Envelope Description
Regular dodecagon

Parallel projection centered on decagonal face.

Trapezium

Parallel projection parallel to square faces and a pair of triangles.

Rectangle

9° side view.

Hendecagon

Parallel projection centered on vertex.

Coordinates

The Cartesian coordinates of the decagonal antiprism, centered on the origin and having edge length 2, are:

where φ = (1+√5)/2 is the Golden Ratio, and H = √(√(11φ+7)−2φ−1), or approximately 0.862397, is half the height of the antiprism.


Last updated 29 May 2018.

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