Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:216AE2of2 GHM

Order: 20

Horizontal side: 216 Vertical side: 216

Elements: 4√2, 8, 8√2, 12√2, 20, 24, 17√2, 20√2, 24√2, 34, 27√2, 34√2, 54, 40√2, 54√2, 88, 108, 81√2, 91√2, 108√2.

Code: 1085 0 108 1084 108 108 916 125 125 170 125 125 542 54 54 541 54 108 272 81 81 881 142 108 402 182 68 810 81 81 246 158 44 342 216 34 126 146 32 245 158 20 343 216 0 40 146 32 87 142 28 80 150 28 204 162 0 203 182 0

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)