Search Results for ""

The biggest little polygon with n sides is the convex plane n-gon of unit polygon diameter having largest possible area. Reinhardt (1922) showed that for n odd, the regular ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The dihedral group D_6 gives the group of symmetries of a regular hexagon. The group generators are given by a counterclockwise rotation through pi/3 radians and reflection ...

A generalized dodecagon is a generalized polygon of order 12. GD(1,2) is the (3,12)-cage graph, more commonly known as the Tutte 12-cage. GD(2,1) is the line graph of the ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

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 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 Kirchhoff index Kf, also simply called the resistance and denoted R (Lukovits et al. 1999), of a connected graph G on n nodes is defined by ...

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...