Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:101AA GHM

Order: 20

Horizontal side: 101 Vertical side: 101

Elements: 2, 2√2, 4, 8√2, 16, 21, 16√2, 25, 19√2, 21√2, 23√2, 24√2, 34, 25√2, 36, 38, 40, 42, 38√2, 40√2.

Code: 405 0 61 404 40 61 210 80 101 211 101 101 230 59 80 421 101 80 367 0 61 26 34 59 47 36 61 343 34 25 25 34 57 162 50 41 244 58 33 190 82 57 163 50 25 82 58 33 380 63 38 381 101 38 255 0 0 254 25 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)