Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:291AA GHM

Order: 20

Horizontal side: 291 Vertical side: 291

Elements: 10, 10√2, 19√2, 38, 44, 32√2, 38√2, 64, 69, 76, 79, 64√2, 69√2, 74√2, 79√2, 114, 133, 143, 148, 158.

Code: 1585 0 133 1481 148 291 742 222 217 1431 291 291 646 158 153 692 291 148 106 148 143 645 158 89 693 291 79 1335 0 0 1141 114 133 765 114 57 441 158 133 324 190 57 103 222 79 790 212 79 791 291 79 385 114 19 384 152 19 194 133 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)