Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:328AA GHM

Order: 20

Horizontal side: 328 Vertical side: 328

Elements: 6√2, 12, 12√2, 24, 19√2, 24√2, 56, 42√2, 56√2, 84, 94, 112, 84√2, 122, 94√2, 103√2, 150, 112√2, 160, 122√2.

Code: 1607 0 328 1120 160 328 1121 272 328 562 328 272 561 328 328 1503 328 122 66 42 210 127 48 216 126 48 204 247 60 216 246 60 192 945 84 122 944 178 122 420 42 210 842 84 84 841 84 168 192 103 103 1224 206 0 1223 328 0 1030 103 103

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)