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  2. Convex uniform honeycomb - Wikipedia

    en.wikipedia.org/wiki/Convex_uniform_honeycomb

    The alternated cubic honeycomb is one of 28 space-filling uniform tessellations in Euclidean 3-space, composed of alternating yellow tetrahedra and red octahedra.. In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.

  3. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these: all 75 nonprismatic uniform polyhedra; a few representatives of the infinite sets of prisms and antiprisms;

  4. Polygon triangulation - Wikipedia

    en.wikipedia.org/wiki/Polygon_triangulation

    A simple polygon is monotone with respect to a line L, if any line orthogonal to L intersects the polygon at most twice. A monotone polygon can be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone. A monotone polygon with n vertices can be triangulated in O(n) time.

  5. Euclidean tilings by convex regular polygons - Wikipedia

    en.wikipedia.org/wiki/Euclidean_tilings_by...

    This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling.

  6. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    For an n-sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as {n/m}. If m is 2, for example, then every second point is joined. If m is 3, then every third point is joined. The boundary of the polygon winds around the center m times. The (non-degenerate) regular stars of up to 12 ...

  7. 120-cell - Wikipedia

    en.wikipedia.org/wiki/120-cell

    Net. In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called a C 120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hecatonicosachoron, dodecacontachoron [1] and hecatonicosahedroid.

  8. Wallace–Bolyai–Gerwien theorem - Wikipedia

    en.wikipedia.org/wiki/Wallace–Bolyai–Gerwien...

    The most common version uses the concept of "equidecomposability" of polygons: two polygons are equidecomposable if they can be split into finitely many triangles that only differ by some isometry (in fact only by a combination of a translation and a rotation). In this case the Wallace–Bolyai–Gerwien theorem states that two polygons are ...

  9. Polygonal turning - Wikipedia

    en.wikipedia.org/wiki/Polygonal_turning

    Polygonal turning (or polygon turning) is a machining process which allows non-circular forms to be machine turned without interrupting the rotation of the raw material. [ 1 ] Technical details