Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:312BD1of2 GHM

Order: 20

Horizontal side: 312 Vertical side: 312

Elements: 4, 4√2, 8, 8√2, 9√2, 18, 14√2, 20, 24, 28, 20√2, 64, 46√2, 110, 78√2, 101√2, 110√2, 156, 202, 156√2.

Code: 2025 0 110 1564 156 156 1563 312 156 464 202 110 206 228 136 647 248 156 786 234 78 86 220 128 205 228 116 183 220 110 85 220 120 285 220 92 44 224 116 43 228 116 241 248 116 1105 0 0 1104 110 0 96 211 101 1010 211 101 144 234 78

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)