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The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the cuboctahedron, octahedron rhombic dodecahedron, and ...

The term "ice fractal" refers to a fractal (square, triangle, etc.) that is based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, ...

An illusion is an object or drawing which appears to have properties which are physically impossible, deceptive, or counterintuitive. Kitaoka maintains a web page of ...

A Meeussen sequence is an increasing sequence of positive integers (m_1, m_2, ...) such that m_1=1, every nonnegative integer is the sum of a subset of the {m_i}, and each ...

A fractal based on iterating the map F(x)=ax+(2(1-a)x^2)/(1+x^2) (1) according to x_(n+1) = by_n+F(x_n) (2) x_(y+1) = -x_n+F(x_(n+1)). (3) The plots above show 10^4 ...

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...

Poincaré's lemma says that on a contractible manifold, all closed forms are exact. While d^2=0 implies that all exact forms are closed, it is not always true that all closed ...

A topological space having a countable dense subset. An example is the Euclidean space R^n with the Euclidean topology, since it has the rational lattice Q^n as a countable ...

The small triakis octahedron graph is Archimedean dual graph which is the skeleton of the small triakis octahedron. It is implemented in the Wolfram Language as ...

A plane curve given by the parametric equations x = cost (1) y = sintsin^m(1/2t). (2) The plots above show curves for values of m from 0 to 7. The teardrop curve has area ...