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There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures), also known as Bakos' compound, ...

A number of attractive cube 6-compounds can be constructed. A first (left figures) is obtained by combining six cubes, each rotated by 1/6 of a turn about the line joining ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

The circumcircle of the Fuhrmann triangle. It has the line HNa, where H is the orthocenter and Na is the Nagel point, as its diameter. In fact, these points (Kimberling ...

The Gibert point can be defined as follows. Given a reference triangle DeltaABC, reflect the point X_(1157) (which is the inverse point of the Kosnita point in the ...

The great truncated cuboctahedron (Maeder 1997), also called the quasitruncated cuboctahedron (Wenninger 1989, p. 145), is the uniform polyhedron with Maeder index 20 (Maeder ...

The great truncated icosidodecahedron, also called the great quasitruncated icosidodecahedron, is the uniform polyhedron with Maeder index 68 (Maeder 1997), Wenninger index ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

A hexagon tiling is a tiling of the plane by identical hexagons. The regular hexagon forms a regular tessellation, also called a hexagonal grid, illustrated above. There are ...