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Polyforms can also be considered in higher dimensions. In 3-dimensional space, basic polyhedra can be joined along congruent faces. Joining cubes in this way produces the polycubes, and joining tetrahedrons in this way produces the polytetrahedrons. 2-dimensional polyforms can also be folded out of the plane along their edges, in similar fashion to a net; in the case of polyominoes, this ...
Edge the facet or (n−1)-face of the polygon; Polyhedron (3-polytope) Vertex the peak or (n−3)-face of the polyhedron; Edge the ridge or (n−2)-face of the ...
A regular digon has both angles equal and both sides equal and is represented by Schläfli symbol {2}. It may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune. The digon is the simplest abstract polytope of rank 2. A truncated digon, t{2} is a square, {4}. An alternated digon, h{2} is a ...
In geometry, a vertex configuration is a shorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex.It has variously been called a vertex description, [1] [2] [3] vertex type, [4] [5] vertex symbol, [6] [7] vertex arrangement, [8] vertex pattern, [9] face-vector, [10] vertex sequence. [11]
The Vatti clipping algorithm [1] is used in computer graphics. It allows clipping of any number of arbitrarily shaped subject polygons by any number of arbitrarily shaped clip polygons . Unlike the Sutherland–Hodgman and Weiler–Atherton polygon clipping algorithms, the Vatti algorithm does not restrict the types of polygons that can be used ...
In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides divided into two ...
A regular polygon can also be represented by its Coxeter-Dynkin diagram, , and its uniform truncation , and its complete truncation . The graph represents Coxeter group I 2 (n), with each node representing a mirror, and the edge representing the angle π/ n between the mirrors, and a circle is given around one or both mirrors to show which ones ...
In geometry, the Wallace–Bolyai–Gerwien theorem, [1] named after William Wallace, Farkas Bolyai and P. Gerwien, is a theorem related to dissections of polygons. It answers the question when one polygon can be formed from another by cutting it into a finite number of pieces and recomposing these by translations and rotations.