Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:148BA GHM

Order: 18

Horizontal side: 148 Vertical side: 148

Elements: 12, 15, 12√2, 18, 15√2, 23, 24, 18√2, 28, 23√2, 27√2, 28√2, 46, 51, 51√2, 74, 97, 74√2.

Code: 975 0 51 744 74 74 743 148 74 234 97 51 233 120 51 282 148 46 281 148 74 517 0 51 510 51 51 274 78 24 150 105 51 151 120 51 463 148 0 120 90 36 121 102 36 182 120 18 181 120 36 241 102 24

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)