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If a polyhedron is not regular, the edge midpoints surrounding a vertex may not be coplanar. However, a form of rectification is still possible in this case: every polyhedron has a polyhedral graph as its 1-skeleton, and from that graph one may form the medial graph by placing a vertex at each edge midpoint of the original graph, and connecting two of these new vertices by an edge whenever ...
In geometry, the rectified truncated icosahedron is a convex polyhedron. It has 92 faces: 60 isosceles triangles , 12 regular pentagons , and 20 regular hexagons . It is constructed as a rectified , truncated icosahedron , rectification truncating vertices down to mid-edges.
In geometry, the rectified truncated octahedron is a convex polyhedron, constructed as a rectified, truncated octahedron. It has 38 faces: 24 isosceles triangles , 6 squares , and 8 hexagons .
This process is known as rectification, making the cuboctahedron being named the rectified cube and rectified octahedron. [3] An alternative construction is by cutting of all of the vertices, known as truncation. can be started from a regular tetrahedron, cutting off the vertices and beveling the edges.
The triangle and squares of the rhombicuboctahedron can be independently rectified or truncated, creating four permutations of polyhedra. The partially truncated forms can be seen as edge contractions of the truncated form. The truncated rhombicuboctahedron can be seen in sequence of rectification and truncation operations from the cuboctahedron.
Dual polyhedra exist in pairs, and the dual of a dual is just the original polyhedron again. Some polyhedra are self-dual, meaning that the dual of the polyhedron is congruent to the original polyhedron. [22] Abstract polyhedra also have duals, obtained by reversing the partial order defining the polyhedron to obtain its dual or opposite order ...
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The dual of a rectified prism is a joined prism or joined bipyramid, in Conway polyhedron notation. The join operation adds vertices at the center of faces, and replaces edges with rhombic faces between original and the neighboring face centers. The joined square prism is the same topology as the rhombic dodecahedron.