Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:450AA GHM

Order: 20

Horizontal side: 450 Vertical side: 450

Elements: 3√2, 6, 6√2, 9√2, 18, 18√2, 30√2, 64, 64√2, 96, 128, 130, 96√2, 160, 128√2, 130√2, 224, 226, 160√2, 290.

Code: 2907 0 450 2263 290 224 1607 290 450 1606 290 290 302 320 260 186 302 242 1302 450 130 96 293 233 185 302 224 30 293 233 67 290 230 60 296 230 646 0 160 1285 64 96 1284 192 96 2243 320 0 645 0 96 1303 450 0 965 0 0 964 96 0

The properties below may precede order:side in a tiling's title:

• c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
• 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. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
• e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
• i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
• r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.

Credit for Discovery

Just three people are credited with the discovery of Primitive Perfects:

Geoffrey H. Morley (GHM, England)

Jasper D. Skinner, II (JDS, United States)

William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)