# Simple Primitive Imperfect Isosceles Right Triangled Squares (SPIIRTS's)

A SPIIRTS is an imperfect isosceles right triangled square with no properly contained pseudotriangle/rectangle/triangle subdivided into 3/2/2 or more elements respectively. Two equal elements may constitute a non-square parallelogram but not a properly contained square.

### Catalogues

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

- pdf of SPIIRTS order 2 (1 tiling) 4k
- pdf of SPIIRTS order 8 (2 tilings) 7k
- pdf of SPIIRTS order 9 (1 tiling) 5k
- pdf of SPIIRTS order 10 (10 tilings) 15k
- pdf of SPIIRTS order 11 (37 tilings) 41k
- pdf of SPIIRTS order 12 (144 tilings) 147k
- pdf of SPIIRTS order 13 (417 tilings) 425k
- pdf of SPIIRTS order 14 (958 tilings) 990k

### Properties

- A tiling is said to be crossed when there is a tile-corner traversed by two lines. There is no known crossed SPIIRTS of order < 15. The properties below may precede "order:side" in a tiling's title:
- 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. The number of pentagons which are degenerate, in the sense that one or more sides have shrunk to zero length, may be 0 (as in 13:15TA and 13:15TB), 1 (as in 11:9TC and 11:10TD) or 2 (as in 8:4TA).
- e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing.
- i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
- z = zigzag by shorter sides of two or more equal tiles, pairs of which form parallelograms.

### Credit for Discovery

The catalogue was built by Geoffrey H. Morley but no SPIIRTS's are attributed to discoverers.