Derivative Ultraperfect Isosceles Right Triangled Squares (DUIRTSs)

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

Catalogues

The DUIRTS catalogues are available as pdfs from this page.

1. pdf of DUIRTSs order 15 (4 tilings) 10k
2. pdf of DUIRTSs order 16 (74 tilings) 87k
3. pdf of DUIRTSs order 17 (342 tilings) 388k
4. pdf of DUIRTSs 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 DUIRTSs of order < 19 are of order 18 and side 147.
• f = as few as two elements in every subquadrilateral.
• 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)