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The Heesch number of a closed plane figure is the maximum number of times that figure can be completely surrounded by copies of itself. The determination of the maximum ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...

The unique (modulo rotations) scalene triangle formed from three vertices of a regular heptagon, having vertex angles pi/7, 2pi/7, and 4pi/7. There are a number of amazing ...

A Heronian tetrahedron, also called a perfect tetrahedron, is a (not necessarily regular) tetrahedron whose sides, face areas, and volume are all rational numbers. It ...

A pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height h is a special case of the formula for a regular n-gonal pyramid with n=6, given by ...

The hexagram is the star polygon {6/2}, also known as the star of David or Solomon's seal, illustrated at left above. It appears as one of the clues in the novel The Da Vinci ...

The Hoffman-Singleton graph is the graph on 50 nodes and 175 edges that is the only regular graph of vertex degree 7, diameter 2, and girth 5. It is the unique (7,5)-cage ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

The hypercube is a generalization of a 3-cube to n dimensions, also called an n-cube or measure polytope. It is a regular polytope with mutually perpendicular sides, and is ...

Let A^' be the outermost vertex of the regular pentagon erected inwards on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...