The Heptagonal Antiprism


The heptagonal antiprism is a 3D uniform polyhedron bounded by 16 polygons (2 heptagons and 14 triangles), 28 edges, and 14 vertices.

The heptagonal
antiprism

Projections

The following are some commonly-encountered views of the heptagonal antiprism:

Projection Description

Heptagon-centered parallel projection.

Parallel to a pair of opposite lateral edges.

Parallel to a pair of opposite triangles.

Vertex-centered parallel projection.

Coordinates

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

where r, A, B, C, D, h, and H are roots of the following polynomials within the indicated ranges:

7r6 − 56r4 + 112r2 − 64 = 0, 2≤r≤3
A3 − A2 − 2A + 1 = 0, 1≤A≤2
7B6 − 21B4 + 14B2 − 1 = 0, 1≤B≤2
C3 − 2C2 − C + 1 = 0, 2≤C≤3
7D6 − 14D4 + 7D2 − 1 = 0, 0≤D≤1
7h6 − 35h4 + 21h2 − 1 = 0, 2≤h≤3
7H6 − 7H4 + 1 = 0, 0.8≤H≤0.9

r and h are the out-radius and in-radius, respectively, of a regular heptagon of edge length 2. H is half the height of the antiprism.

Their approximate values are:


Last updated 24 Jul 2020.

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