# 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.

- pdf of DUIRTSs order 15 (4 tilings) 10k
- pdf of DUIRTSs order 16 (74 tilings) 87k
- pdf of DUIRTSs order 17 (342 tilings) 388k
- 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)