Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:184AC3of4 GHM

Order: 18

Horizontal side: 184 Vertical side: 184

Elements: 8√2, 10√2, 16, 20, 16√2, 32, 24√2, 40, 30√2, 31√2, 32√2, 40√2, 62, 51√2, 82, 72√2, 102, 92√2.

Code: 1025 0 82 924 92 92 726 112 112 203 112 92 322 144 80 104 102 82 306 82 62 825 0 0 514 51 31 323 144 48 402 184 40 316 51 31 625 82 0 165 112 32 164 128 32 246 120 24 403 184 0 84 120 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)