Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:456AR GHM

Order: 20

Horizontal side: 456 Vertical side: 456

Elements: 6, 8, 6√2, 8√2, 12, 16, 12√2, 18√2, 21√2, 42, 55√2, 110, 118, 152, 110√2, 194, 152√2, 228, 304, 228√2.

Code: 3045 0 152 2284 228 228 2283 456 228 554 283 173 163 338 212 82 346 220 1181 456 228 83 346 212 1102 456 110 180 322 212 124 334 200 123 346 200 64 340 194 63 346 194 216 283 173 427 304 194 1943 346 0 1525 0 0 1524 152 0 1103 456 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)