Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:204AI GHM

Order: 20

Horizontal side: 204 Vertical side: 204

Elements: 2√2, 4, 4√2, 6, 6√2, 12, 12√2, 13√2, 26, 19√2, 20√2, 38, 32√2, 64, 76, 64√2, 70√2, 76√2, 128, 102√2.

Code: 1285 0 76 1024 102 102 706 134 134 196 115 115 385 134 96 130 115 115 261 128 102 65 128 96 42 132 92 41 132 96 22 134 94 204 152 76 320 172 96 60 134 94 127 128 88 120 140 88 765 0 0 764 76 0 640 140 64 641 204 64

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)