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As defined by Kyrmse, a canonical polygon is a closed polygon whose vertices lie on a point lattice and whose edges consist of vertical and horizontal steps of unit length or ...

The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line ...

A description of an object by properties that are different from those mentioned in its definition, but are equivalent to them. The following list gives a number of examples. ...

The mapping of a grid of regularly ruled squares onto a cone with no overlap or misalignment. Cone nets are possible for vertex angles of 90 degrees, 180 degrees, and 270 ...

Conway triangle notation defines S=2Delta (1) where Delta is the area of a reference triangle, and S_phi=Scotphi. (2) This gives the special cases S_A = 1/2(-a^2+b^2+c^2) (3) ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

The total angular defect is the sum of the angular defects over all polyhedron vertices of a polyhedron, where the angular defect delta at a given polyhedron vertex is the ...

The diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(76). This solid is the diminished polyhedron obtained by diminishing a small ...

A compound of five regular dodecahedra with the symmetry of the icosahedron (Wenninger 1983, pp. 145-147) can be constructed by taking a dodecahedron with top and bottom ...