Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AC GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 10, 12, 10√2, 20, 20√2, 30√2, 41√2, 70, 53√2, 76, 82, 88, 94, 100, 106, 76√2, 82√2, 88√2, 94√2, 100√2.

Code: 1067 0 270 760 106 270 761 182 270 887 182 270 886 182 182 300 30 194 204 50 174 203 70 174 1007 70 194 1000 170 194 121 182 194 104 60 164 103 70 164 822 82 82 701 70 164 534 123 41 940 176 94 941 270 94 823 82 0 412 123 41

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)