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Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. The dihedral angles for the ... Octahedron {3,4} (3.3.3.3)
It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes. It contains the 75 nonprismatic uniform polyhedra , as well as 44 stellated forms of the convex regular and quasiregular polyhedra.
Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron , which has eight triangular faces. Because of the ambiguity of the term octahedron and tilarity of the various eight-sided figures, the term is rarely used without clarification.
The ideal tetrahedron, cube, octahedron, and dodecahedron form respectively the order-6 tetrahedral honeycomb, order-6 cubic honeycomb, order-4 octahedral honeycomb, and order-6 dodecahedral honeycomb; here the order refers to the number of cells meeting at each edge. However, the ideal icosahedron does not tile space in the same way.
Example: an octahedron is a birectification of a cube: {3,4} = 2r{4,3}. Another type of truncation, cantellation , cuts edges and vertices, removing the original edges, replacing them with rectangles, removing the original vertices, and replacing them with the faces of the dual of the original regular polyhedra or tiling.
Stella: Polyhedron Navigator – Software able to generate and print nets for all uniform polyhedra. Used to create most images on this page. Paper models; Uniform indexing: U1-U80, (Tetrahedron first) Uniform Polyhedra (80), Paul Bourke; Weisstein, Eric W. "Uniform Polyhedron".
The deltoidal icositetrahedron is a member of a family of duals to the uniform polyhedra related to the cube and regular octahedron. When projected onto a sphere (see right), it can be seen that the edges make up the edges of a cube and regular octahedron arranged in their dual positions. It can also be seen that the 3- and 4-fold corners can ...
In geometry, a hemi-octahedron is an abstract regular polyhedron, containing half the faces of a regular octahedron. It has 4 triangular faces, 6 edges, and 3 vertices. Its dual polyhedron is the hemicube .