Primitive Perfect Isosceles Right Triangled Square

Title: _d 18:94BD2of2 GHM

Order: 18

Horizontal side: 94 Vertical side: 94

Elements: 2, 2√2, 4, 4√2, 10, 12, 10√2, 15, 15√2, 16√2, 17√2, 30, 31, 32, 31√2, 47, 63, 47√2.

Code: 635 0 31 474 47 47 473 94 47 164 63 31 303 79 17 152 94 32 151 94 47 323 94 0 317 0 31 310 31 31 121 43 31 105 43 21 104 53 21 27 43 21 26 43 19 45 45 17 44 49 17 174 62 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)