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2. Icosahedron - Wikipedia

   en.wikipedia.org/wiki/Icosahedron

   In Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, the 12 isosceles faces are arranged differently so that the figure is non-convex and has right dihedral angles. It is scissors congruent to a cube, meaning that it can be sliced into smaller polyhedral pieces that can be rearranged to form a solid cube.

3. Hexagon - Wikipedia

   en.wikipedia.org/wiki/Hexagon

   A regular hexagon has Schläfli symbol {6} [2] and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges.. A regular hexagon is defined as a hexagon that is both equilateral and equiangular.

4. Tetrahedral-octahedral honeycomb - Wikipedia

   en.wikipedia.org/wiki/Tetrahedral-octahedral...

   The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space.It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2.

5. Uniform polyhedron - Wikipedia

   en.wikipedia.org/wiki/Uniform_polyhedron

   Coxeter, Longuet-Higgins & Miller (1954) define uniform polyhedra to be vertex-transitive polyhedra with regular faces. They define a polyhedron to be a finite set of polygons such that each side of a polygon is a side of just one other polygon, such that no non-empty proper subset of the polygons has the same property.

6. Void Cube - Wikipedia

   en.wikipedia.org/wiki/Void_Cube

   On the regular cube a 90˚ rotation of the whole cube about a principal axis swaps the positions of 24 pieces in six, odd parity, four cycles. On the regular cube a whole cube rotation is an even permutation. On the other hand, lacking center pieces, a 90˚ whole cube rotation on the Void Cube swaps 20 pieces in five, odd parity, four cycles.

7. Convex hull algorithms - Wikipedia

   en.wikipedia.org/wiki/Convex_hull_algorithms

   Algorithms that construct convex hulls of various objects have a broad range of applications in mathematics and computer science.. In computational geometry, numerous algorithms are proposed for computing the convex hull of a finite set of points, with various computational complexities.

8. Polyhedral combinatorics - Wikipedia

   en.wikipedia.org/wiki/Polyhedral_combinatorics

   For instance, a cube has eight vertices, twelve edges, and six facets, so its ƒ-vector is (8,12,6). The dual polytope has a ƒ-vector with the same numbers in the reverse order; thus, for instance, the regular octahedron, the dual to a cube, has the ƒ-vector (6,12,8).

9. Planar graph - Wikipedia

   en.wikipedia.org/wiki/Planar_graph

   A planar graph is said to be convex if all of its faces (including the outer face) are convex polygons. Not all planar graphs have a convex embedding (e.g. the complete bipartite graph K 2,4 ). A sufficient condition that a graph can be drawn convexly is that it is a subdivision of a 3-vertex-connected planar graph.