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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.
In a face centered cubic structure, an octahedral interstitial site is highlighted in red, and a tetrahedral interstitial site is highlighted in blue. Réalisé avec/made with : Inkscape. Voir aussi/see also. Image:Sites interstitiels empilement compact.svg
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Coxeter, Longuet-Higgins & Miller (1954) define uniform polyhedra to be vertex-transitive polyhedra with regular faces. They define a polyhedron to be a finite set of polygons such that each side of a polygon is a side of just one other polygon, such that no non-empty proper subset of the polygons has the same property.
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.
bicapped trigonal prismatic [ZrF 8] 4− [7] PuBr 3 [3] 8 cubic: Caesium chloride, calcium fluoride: 8 hexagonal bipyramidal: N in Li 3 N [3] 8 octahedral, trans-bicapped Ni in nickel arsenide, NiAs; 6 As neighbours + 2 Ni capping [8] 8 trigonal prismatic, triangular face bicapped Ca in CaFe 2 O 4 [3] 9 tricapped trigonal prismatic
(Cantellated tetrahedral-octahedral honeycomb) or : Truncated triangular pyramid: Quarter cubille: irr. triangular bipyramid: J 24 A 20 W 16 G 21 h 2,3 δ 4 fc [4,3 1,1] f-tCO-trille (Cantitruncated tetrahedral-octahedral honeycomb) or : Mirrored sphenoid: Half pyramidille: Mirrored sphenoid: J 25,33 A 13 W 10 G 6 qδ 4 d [[3 [4]]] Truncated ...
A high-index reflective subgroup is the prismatic octahedral symmetry, [4,3,2] (), order 96, subgroup index 4, (Du Val #44 (O/C 2;O/C 2) *, Conway ± 1 / 24 [O×O].2). The truncated cubic prism has this symmetry with Coxeter diagram and the cubic prism is a lower symmetry construction of the tesseract, as .