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Polycairos are polyforms obtained from the Cairo tessellation, illustrated above. The numbers of polycairos with n=1, 2, ... components are 1, 2, 5, 17, 55, 206, 781, 3099, ...

Let c=(c_1,...,c_n) be a point in C^n, then the open polydisk is defined by S={z:|z_j-c_j|<|z_j^0-c_j|} for j=1, ..., n.

A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) are x^_ = ...

The diameter of a polygon is the largest distance between any pair of vertices. In other words, it is the length of the longest polygon diagonal (e.g., straight line segment ...

The breaking up of self-intersecting polygons into simple polygons (illustrated above) is also called tessellation (Woo et al. 1999).

A polygrammic prism is a prism formed by two regular polygrams offset along their symmetry axis and with corresponding edges connected by lateral faces. The hexagrammic prism ...

A line segment where two faces of a polyhedron meet, also called a side.

A point at which three or more polyhedron edges of a polyhedron meet. The concept can also be generalized to a polytope.

A curve obtained by fitting polynomials to each ordinate of an ordered sequence of points. The above plots show polynomial curves where the order of the fitting polynomial ...