Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:178AC GHM

Order: 20

Horizontal side: 178 Vertical side: 178

Elements: 5, 5√2, 10, 15, 20, 35, 25√2, 27√2, 29√2, 31√2, 35√2, 54, 58, 62, 54√2, 56√2, 58√2, 85, 62√2, 66√2.

Code: 625 0 116 624 62 116 276 97 151 547 124 178 546 124 124 660 97 151 582 58 58 314 31 85 564 87 29 853 143 0 252 168 60 201 163 85 155 163 70 57 163 70 56 163 65 107 168 70 356 143 35 583 58 0 292 87 29 355 143 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)