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.
Projections
The following are some commonlyencountered views of the heptagonal antiprism:
Projection  Description 

Heptagoncentered parallel projection. 

Parallel to a pair of opposite lateral edges. 

Parallel to a pair of opposite triangles. 

Vertexcentered parallel projection. 
Coordinates
The Cartesian coordinates of the heptagonal antiprism, centered on the origin and having edge length 2, are:
 (0, r, H)
 (±A, B, H)
 (±C, −D, H)
 (±1, −h, H)
 (0, −r, −H)
 (±A, −B, −H)
 (±C, D, −H)
 (±1, h, −H)
where r, A, B, C, D, h, and H are roots of the following polynomials within the indicated ranges:
7r^{6} − 56r^{4} + 112r^{2} − 64 = 0,  2≤r≤3 
A^{3} − A^{2} − 2A + 1 = 0,  1≤A≤2 
7B^{6} − 21B^{4} + 14B^{2} − 1 = 0,  1≤B≤2 
C^{3} − 2C^{2} − C + 1 = 0,  2≤C≤3 
7D^{6} − 14D^{4} + 7D^{2} − 1 = 0,  0≤D≤1 
7h^{6} − 35h^{4} + 21h^{2} − 1 = 0,  2≤h≤3 
7H^{6} − 7H^{4} + 1 = 0,  0.8≤H≤0.9 
r and h are the outradius and inradius, respectively, of a regular heptagon of edge length 2. H is half the height of the antiprism.
Their approximate values are:
 r = 2.304764870962486
 A = 1.801937735804838
 B = 1.436997392727370
 C = 2.246979603717467
 D = 0.512858431636277
 h = 2.076521396572336
 H = 0.858473196494555