The Heptagonal Prism

---

The heptagonal prism is a 3D uniform polyhedron bounded by 9 polygons (2 heptagons and 7 squares), 21 edges, and 14 vertices. It may be considered to be the extrusion of the heptagon.

Projections

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

Projection	Description
	Top view.
	Front view.
	Side-view.
	Vertex-centered parallel projection.

Coordinates

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

• (0, r, ±1)
• (±A, B, ±1)
• (±C, −D, ±1)
• (±1, −h, ±1)

where r, A, B, C, D, 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

r and h are the out-radius and in-radius, respectively, of a regular heptagon of edge length 2.

Their approximate values are:

• r = 2.304764870962486
• A = 1.801937735804838
• B = 1.436997392727370
• C = 2.246979603717467
• D = 0.512858431636277
• h = 2.076521396572336