Decagonal prism

The decagonal prism, or dip, is a prismatic uniform polyhedron. It consists of 2 decagons and 10 squares. Each vertex joins one decagon and two squares. As the name suggests, it is a prism based on a decagon.

Vertex coordinates
A decagonal prism of edge length 1 has vertex coordinates given by:
 * (±1/2, ±$\sqrt{7+2√5}$/2, ±1/2),
 * (±(3+$\sqrt{5+2√5}$)/4, ±$\sqrt{2}$, ±1/2),
 * (±(1+$\sqrt{2}$)/2, 0, ±1/2).

Representations
A decagonal prism has the following Coxeter diagrams:


 * x x10o (full symmetry)
 * x x5x (as dipentagonal prism)
 * s2s10x (as dipentagonal trapezoprism)
 * xx10oo&#x (decagonal frustum)
 * xx5xx&#x (dipentagonal frustum)
 * xxxxx xFVFx&#xt (A1×A1 axial, square-first)

Variations
There are several isogonal lower-symmetry variants of the decagonal prism, all of which are listed below:

Dipentagonal prism
A dipentagonal prism is a prism based on a dipentagon. The two bases are dipentagons, while the lateral sides are 5+5 rectangles.

Dipentagonal trapezoprism
A dipentagonal trapezoprism is made out of two opposite dipentagons in parallel planes, connected by 10 isosceles trapezoids.

Related polyhedra
A number of Johnson solids can be formed by attaching various configurations of pentagonal cupolas and pentagonal rotundas to the bases of the decagonal prism:


 * Elongated pentagonal cupola - Cupola attached to one base
 * Elongated pentagonal rotunda - Rotunda attached to one base
 * Elongated pentagonal orthobicupola - Cupolas in same orientation attached to both bases
 * Elongated pentagonal gyrobicupola - Cupolas rotated by 36º attached to bases
 * Elongated pentagonal orthocupolarotunda - Cpuola attached to one base, rotunda with same pentagon orientation attached to other base
 * Elongated pentagonal gyrocupolarotunda - Cupola attached to one base, rotunda with pentagon rotated by 36º attached to other base
 * Elongated pentagonal orthobirotunda - Rotundas in same orientation attached to both bases
 * Elongated pentagonal gyrobirotunda - Rotundas rotated by 36º attached to bases

The rhombisnub dodecahedron is a uniform polyhedron compound composed of 6 decagonal prisms.