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The two octahedral cells project onto the entire volume of this envelope, while the 8 triangular prismic cells project onto its 8 triangular faces. The triangular-prism-first orthographic projection of the octahedral prism into 3D space has a hexagonal prismic envelope. The two octahedral cells project onto the two hexagonal faces.
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A prismatic polytope is a Cartesian product of two polytopes of lower dimension; familiar examples are the 3-dimensional prisms, which are products of a polygon and a line segment. The prismatic uniform 4-polytopes consist of two infinite families: Polyhedral prisms: products of a line segment and a uniform polyhedron.
[C] Coxeter et al., 1954, showed the convex forms as figures 15 through 32; three prismatic forms, figures 33–35; and the nonconvex forms, figures 36–92. [ W ] Wenninger, 1974, has 119 figures: 1–5 for the Platonic solids, 6–18 for the Archimedean solids, 19–66 for stellated forms including the 4 regular nonconvex polyhedra, and ended ...
In four-dimensional geometry, a prismatic uniform 4-polytope is a uniform 4-polytope with a nonconnected Coxeter diagram symmetry group. [ citation needed ] These figures are analogous to the set of prisms and antiprism uniform polyhedra, but add a third category called duoprisms , constructed as a product of two regular polygons.
Buckminster Fuller's Dymaxion map. A polyhedral map projection is a map projection based on a spherical polyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon or other shape in the plane. The best-known polyhedral map projection is Buckminster Fuller's Dymaxion map.
Prismatic uniform polyhedron: Elements: F = 10, ... octagonal prisms are used to generate flicker-free images in movie projectors. ... By using this site, ...
The Waterman "Butterfly" World Map is a map projection created by Steve Waterman. Waterman first published a map in this arrangement in 1996. The arrangement is an unfolding of a polyhedral globe with the shape of a truncated octahedron, evoking the butterfly map principle first developed by Bernard J.S. Cahill (1866–1944) in 1909