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The ridges of a 2D polygon or 1D tiling are its 0-faces or vertices. The ridges of a 3D polyhedron or plane tiling are its 1-faces or edges. The ridges of a 4D polytope or 3-honeycomb are its 2-faces or simply faces. The ridges of a 5D polytope or 4-honeycomb are its 3-faces or cells.
The white polygon lines represent the "vertex figure" polygon. The colored faces are included on the vertex figure images help see their relations. Some of the intersecting faces are drawn visually incorrectly because they are not properly intersected visually to show which portions are in front.
Peak, an (n-3)-dimensional element For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices.
A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids , prisms (and other polyhedrons ), cubes , cylinders , cones (and truncated cones ).
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
In three-dimensional geometry, a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face. [1] [2] To facet a polyhedron is to find and join such facets to form the faces of a new polyhedron; this is the reciprocal process to stellation and may also be applied to higher-dimensional polytopes. [3]