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Let A_1, A_2, A_3, and A_4 be four points on a circle, and H_1, H_2, H_3, H_4 the orthocenters of triangles DeltaA_2A_3A_4, etc. If, from the eight points, four with ...

The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated above in a number of embeddings. It is denoted F_(032)A in the Foster census of cubic symmetric graphs ...

The endodocehedron, also called the concave pyrohedral dodecahedron, is the concave solid corresponding to the interior void formed when each face of a regular dodecahedron ...

An Enriques surface X is a smooth compact complex surface having irregularity q(X)=0 and nontrivial canonical sheaf K_X such that K_X^2=O_X (Endraß). Such surfaces cannot be ...

Euler conjectured that there do not exist Euler squares of order n=4k+2 for k=1, 2, .... In fact, MacNeish (1921-1922) published a purported proof of this conjecture (Bruck ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

Four line geometry is a finite geometry subject to the following three axioms: 1. there exist exactly four lines, 2. any two distinct lines have exactly one point of on both ...

The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus ...

A golden rhombohedron is a rhombohedron whose faces consist of congruent golden rhombi. Golden rhombohedra are therefore special cases of a trigonal trapezohedron as well as ...

The granny knot is a composite knot of six crossings consisting of a knot sum of two left-handed trefoils with the same orientation (Rolfsen 1976, p. 220). The granny knot ...