Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:341AA GHM

Order: 20

Horizontal side: 341 Vertical side: 341

Elements: 16, 16√2, 32, 31√2, 32√2, 38√2, 63, 64, 76, 63√2, 64√2, 77√2, 88√2, 125, 126, 138, 152, 108√2, 176, 139√2.

Code: 1527 0 341 880 152 341 1261 278 341 632 341 278 631 341 341 1396 202 139 646 0 189 1767 64 253 380 240 253 1383 202 77 767 202 215 645 0 125 312 233 108 1255 0 0 324 32 93 323 64 93 1080 233 108 164 48 77 163 64 77 774 125 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)