Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:186BI GHM

Order: 20

Horizontal side: 186 Vertical side: 186

Elements: 6, 6√2, 12, 14, 12√2, 24, 17√2, 28, 31, 24√2, 34, 45, 48, 38√2, 62, 76, 55√2, 62√2, 124, 93√2.

Code: 1245 0 62 934 93 93 556 131 131 380 131 131 311 124 93 457 124 93 170 169 93 283 152 48 347 152 76 763 186 0 625 0 0 624 62 0 143 124 48 483 110 0 242 134 24 241 134 48 122 146 36 121 146 48 62 152 42 61 152 48

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)