# Non-ultraperfect Perfect Isosceles Right Triangled Squares (NPIRTSs)

An NPIRTS is a perfect isosceles right triangled square (perfect IRTS) which is a subdivision of an imperfect IRTS. The lowest order of an NPIRTS which does not have an unbroken main diagonal is 16. Every NPIRTS below order 16 is a subdivision of SPIIRTS 2:1TA.

### Catalogues

The NPIRTS catalogues are available as pdfs from this page.

- pdf of NPIRTSs order 7 (2 tilings) 3.8Kb
- pdf of NPIRTSs order 8 (4 tilings) 5.4Kb
- pdf of NPIRTSs order 9 (23 tilings) 20.6Kb
- pdf of NPIRTSs order 10 (101 tilings) 86.2Kb
- pdf of NPIRTSs order 11 (354 tilings) 305.5Kb
- pdf of NPIRTSs order 12 (1326 tilings) 1.1MB

### Properties

The fact that every NPIRTS has a subdivided triangle is not recorded as a property. The properties below may precede "order:side" in a tiling's title:

- e = elegant. No tiling is just a T-junction. Such tilings may be considered aesthetically pleasing.
- p/r = pseudotriangular/rectangular inclusion subdivided into at least 6/5 triangles respectively.

### Credit for Discovery

Jasper D. Skinner found many NPIRTSs before this catalogue was built by Geoffrey H. Morley. Only the two lowest order NPIRTSs are attributed to discoverers:

J. Douglas and E.P. Starke (**D&S**, United States) (7:10PA only)

Arthur H. Stone (**AHS**, United States, 1916-2000) (7:7PA only)