Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:158AE4of4 GHM

Order: 20

Horizontal side: 158 Vertical side: 158

Elements: 4√2, 8, 8√2, 10√2, 16, 12√2, 13√2, 20, 16√2, 26, 20√2, 23√2, 46, 33√2, 56, 46√2, 66, 56√2, 102, 79√2.

Code: 1025 0 56 794 79 79 663 158 92 136 79 79 267 92 92 163 118 76 82 126 84 81 126 92 42 130 88 164 142 76 466 112 46 120 130 88 106 92 66 205 102 56 204 122 56 567 0 56 560 56 56 334 89 23 236 89 23 465 112 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)