Search results
Results from the WOW.Com Content Network
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.
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.
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 polyhedron is topologically related as a part of a sequence of cantellated polyhedra with vertex figure (3.4.n.4), which continues as tilings of the hyperbolic plane. These vertex-transitive figures have (*n32) reflectional symmetry .
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent . Uniform polyhedra may be regular (if also face- and edge-transitive ), quasi-regular (if also edge-transitive but not face-transitive), or semi-regular ...
The excavated truncated rhombicuboctahedron is a toroidal polyhedron, constructed from a truncated rhombicuboctahedron with its 12 irregular octagonal faces removed.It comprises a network of 6 square cupolae, 8 triangular cupolae, and 24 triangular prisms.
:-) One thing for sure, in 4D there is a new kind of truncation. Consider the progressive truncation of the cube into the octahedron: you go from cube -> truncated cube -> cuboctahedron (rectified cube/octahedron) -> truncated octahedron -> octahedron. So in 3D, the rectified polyhedron is sorta of "midpoint" between two duals.