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In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself. More specifically: More specifically: In three-dimensional geometry, a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face .
Facet, an (n-1)-dimensional element; Ridge, an (n-2)-dimensional element; 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.
Example of a low poly triangle mesh representing a dolphin. In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edge s and face s that defines the shape of a polyhedral object's surface.
In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.. New edges of a faceted polyhedron may be created along face diagonals or internal space diagonals.
In elementary geometry, a face is a polygon [note 1] on the boundary of a polyhedron. [3] [4] Other names for a polygonal face include polyhedron side and Euclidean plane tile. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2-dimensional features of a 4-polytope.
A facet-transitive or isotopic figure is an n-dimensional polytope or honeycomb with its facets ((n−1)-faces) congruent and transitive. The dual of an isotope is an isogonal polytope. By definition, this isotopic property is common to the duals of the uniform polytopes .
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One such facet is shown in as seen in this Poincaré disk model. In H 3 hyperbolic space, paracompact regular honeycombs have Euclidean tiling facets and vertex figures that act like finite polyhedra. Such tilings have an angle defect that can be closed by bending one way or the other.