Decagonal-dodecagonal duoprismatic prism

{{Infobox polytope The decagonal-dodecagonal duoprismatic prism or datwip, also known as the decagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 decagonal-dodecagonal duoprisms, 10 square-dodecagonal duoprisms, and 12 square-decagonal duoprisms. Each vertex joins 2 square-decagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 decagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.
 * type=Uniform
 * dim = 5
 * img=
 * off = auto
 * obsa = Datwip
 * coxeter = x x10o x12o
 * army = Datwip
 * reg = Datwip
 * terons = 12 square-decagonal duoprisms, 10 square-dodecagonal duoprisms, 2 decagonal-dodecagonal duoprisms
 * cells = 120 cubes, 10+20 dodecagonal prisms, 12+24 decagonal prisms
 * faces = 120+120+240 squares, 24 decagons, 20 dodecagons
 * edges = 120+240+240
 * vertices = 240
 * circum = $$\frac{\sqrt{15+4\sqrt3+2\sqrt5}}2 ≈ 2.56906$$
 * hypervol = $$\frac{15\sqrt{35+20\sqrt3+14\sqrt5+8\sqrt{15}}{2} ≈ 86.14553$$
 * dit = Squadedip–dip–squadedip: 150°
 * dit2 = Sitwadip–twip–sitwadip: 144°
 * dit3 = Sitwadip–cube–squadedip: 90°
 * dit4 = Datwadip–dip–squadedip: 90°
 * dit5 = Sitwadip–twip–datwadip: 90°
 * height = 1
 * verf = Digonal disphenoidal pyramid, edge lengths $\sqrt{(5+√5)/2}$ (disphenoid base 1), $\sqrt{2+√3}$ (disphenoid base 2), $\sqrt{2}$ (remaining edges)
 * symmetry = I{{sub|2}}(10)×I{{sub|2}}(12)×A{{sub|1}}, order 960
 * pieces = 24
 * loc = 30
 * dual=Decagonal-dodecagonal duotegmatic tegum
 * conjugate = Decagonal-dodecagrammic duoprismatic prism, Decagrammic-dodecagonal duoprismatic prism, Decagrammic-dodecagrammic duoprismatic prism
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

This polyteron can be alternated into a pentagonal-hexagonal duoantiprismatic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pentagonal-hexagonal prismatic prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of a decagonal-dodecagonal duoprismatic prism of edge length 1 are given by all permutations of the third and fourth coordinates of:
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right).$$

Representations
A decagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:
 * x x10o x12o (full symmetry)
 * x x5x x12o (decagons as dipentagons)
 * x x10o x6x (dodecagons as dihexagons)
 * x x5x x6x
 * xx10oo xx12oo&#x (decagonal-hendecagonal duoprism atop decagonal-hendecagonal duoprism)
 * xx5xx xx12oo&#x
 * xx10oo xx6xx&#x
 * xx5xx xx6xx&#x