Derivative Ultraperfect Isosceles Right Triangled Squares (DUIRTS's)

A DUIRTS is a perfect isosceles right triangled square (perfect IRTS) which is neither primitive nor a subdivision of an imperfect IRTS.

Catalogues

Individual tilings are accessible from the menus on the left. All collections of tilings can also be downloaded. The DUIRTS catalogues are available as pdfs from this page.

1. pdf of DUIRTS's order 15 (4 tilings) 10k
2. pdf of DUIRTS's order 16 (74 tilings) 87k
3. pdf of DUIRTS's order 17 (342 tilings) 388k
4. pdf of DUIRTS's order 18 (1841 tilings) 2.1M

Properties

The properties below may precede "order:side" in a tiling's title:

• c = crossed. There is a tile-corner traversed by two lines. 18:48JB2of5 is the only known crossed DUIRTS of order < 19.
• d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles.
• e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant DUIRTS's of order < 19 are of order 18 and side 147.
• p/r/t = pseudotriangular/rectangular/triangular inclusion subdivided into at least 6/5/6 triangles respectively.

Credit for Discovery

Geoffrey H. Morley (GHM, England)

Jasper D. Skinner, II (JDS, United States)