Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272BD GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 4, 4√2, 8, 6√2, 8√2, 12√2, 17√2, 28, 20√2, 34, 34√2, 68, 96, 68√2, 102, 85√2, 88√2, 96√2, 170, 176.

Code: 1765 0 96 1701 170 272 852 255 187 1021 272 272 170 255 187 340 238 170 341 272 170 283 204 108 687 204 136 686 204 68 66 170 102 47 176 108 40 180 108 124 192 96 206 184 88 87 176 104 80 184 104 965 0 0 964 96 0 880 184 88

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)