Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272BG GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 2√2, 4, 4√2, 6√2, 12, 12√2, 24, 22√2, 23√2, 44, 46, 45√2, 68, 90, 92, 114, 90√2, 92√2, 180, 136√2.

Code: 1805 0 92 1364 136 136 1143 272 158 220 158 158 461 204 158 232 227 135 681 272 158 441 180 136 245 180 112 450 227 135 125 180 100 124 192 100 42 184 96 64 186 94 43 184 92 22 186 94 925 0 0 924 92 0 900 182 90 901 272 90

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)