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In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; [1] a three-dimensional solid bounded exclusively by faces is a polyhedron. A face can be finite like a polygon or circle, or infinite like a half-plane or plane.
A convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid [3]. Some authors exclude uniform polyhedra from the definition. A uniform polyhedron is a polyhedron in which the faces are regular and they are isogonal ; examples include Platonic and Archimedean solids as well as ...
A Johnson solid is a convex polyhedron whose faces are all regular polygons. [1] Here, a polyhedron is said to be convex if the shortest path between any two of its vertices lies either within its interior or on its boundary, none of its faces are coplanar (meaning they do not share the same plane, and do not "lie flat"), and none of its edges are colinear (meaning they are not segments of the ...
The Kleetope of a polyhedron is a new polyhedron made by replacing each face of the original with a pyramid, and so the faces of a Kleetope will be triangles. [15] More generally, triangles can be found in higher dimensions, as in the generalized notion of triangles known as the simplex , and the polytopes with triangular facets known as the ...
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 ...
In geometry, a tractrix (from Latin trahere 'to pull, drag'; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a pulling point (the tractor) that moves at a right angle to the initial line between the object and the puller at an ...