Octahedron template5/8/2023 ![]() It is one of only four 4-connected simplicial well-covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size. The octahedron is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices. If the edge length of a regular octahedron is a, the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is It is a moderately difficult model to construct. A truncated octahedron is an Archimedean solid comprised of 8 regular hexagonal faces, 6 regular square faces, 24 vertices and 36 edges. It is also a triangular antiprism in any of four orientations.Īn octahedron is the three-dimensional case of the more general concept of a cross polytope.Ī regular octahedron is a 3-ball in the Manhattan ( ℓ 1) metric. Develop cognitive and geometric abilities through paper model building. It is a square bipyramid in any of three orthogonal orientations. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.Ī regular octahedron is the dual polyhedron of a cube. Orthographic projections and Schlegel diagrams with Hamiltonian cycles of the vertices of the five platonic solids only the octahedron has an Eulerian. Tip: If you want, the glue tabs can be folded downĪnd glued to a face or trimmed to one-eighth of an inch.In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces.
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