Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:188AB GHM

Order: 18

Horizontal side: 188 Vertical side: 188

Elements: 3√2, 6, 6√2, 12, 14, 12√2, 14√2, 28, 21√2, 38, 28√2, 56, 66, 80, 94, 108, 80√2, 94√2.

Code: 1085 0 80 944 94 94 943 188 94 144 108 80 143 122 80 385 122 56 661 188 94 807 0 80 800 80 80 214 101 59 126 110 68 66 104 62 125 110 56 36 101 59 65 104 56 561 160 56 282 188 28 283 188 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)