Non-ultraperfect Perfect Isosceles Right Triangled Squares (NPIRTS's)

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

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

1. pdf of NPIRTS's order 7 (2 tilings) 6k
2. pdf of NPIRTS's order 8 (4 tilings) 8k
3. pdf of NPIRTS's order 9 (23 tilings) 27k
4. pdf of NPIRTS's order 10 (101 tilings) 99k
5. pdf of NPIRTS's order 11 (354 tilings) 343k
6. pdf of NPIRTS's order 12 (1326 tilings) 1.3M

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 NPIRTS's before this catalogue was built by Geoffrey H. Morley. Only the two lowest order NPIRTS's 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)