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.


The NPIRTS catalogues are available as pdfs from this page.

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


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:

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)