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For questions about mathematical tiling.

1 vote

Tiling with ten-fold symmetry and (unoriented) Penrose tiles?

The division of a pentagon into triangular pieces described here can be used to generate a tenfold quasilattice. At each node generated by any iteration additional edges are rendered in subsequent ite …
Oscar Lanzi's user avatar
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6 votes

Can the sphere be partitioned into small congruent cells?

Also the quadrilateral is indeed relatively "thin" because of the $36°$ vertex angle, which cannot be avoided in an icosahedrally symmetric 120-cell tiling. …
Oscar Lanzi's user avatar
  • 2,370
2 votes

Dividing a square into 5 equal squares

The same as other answers, but rendered in terms of origami to define the cut lines. Label the corners $A,B,C,D$ in rotational order. Then fold and unfold $AB$ onto $DC$ and from this fold identify $A …
Oscar Lanzi's user avatar
  • 2,370