Golygon

The number of golygons for a given permissible value of n may be computed efficiently using generating functions (sequence A007219 in the OEIS).

There is a unique eight-sided golygon (shown in the figure); it can tile the plane by 180-degree rotation using the Conway criterion.

A serial-sided isogon of order n is a closed polygon with a constant angle at each vertex and having consecutive sides of length 1, 2, ..., n units.

[5] A spirolateral is similar construction, notationally nθi1,i2,...,ik which sequences lengths 1,2,3,...,n with internal angles θ, with option of repeating until it returns to close with the original vertex.

The three-dimensional generalization of a golygon is called a golyhedron – a closed simply-connected solid figure confined to the faces of a cubical lattice and having face areas in the sequence 1, 2, ..., n, for some integer n, first introduced in a MathOverflow question.

The smallest golygon has 8 sides. It is the only solution with fewer than 16 sides. It contains two concave corners, and fits on an 8×10 grid. It is also a spirolateral , 8 90° 1,5 .