Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:106BA GHM

Order: 19

Horizontal side: 106 Vertical side: 106

Elements: 3√2, 5, 6, 5√2, 10, 10√2, 15, 13√2, 15√2, 16√2, 25, 18√2, 19√2, 34, 38, 34√2, 53, 72, 53√2.

Code: 725 0 34 534 53 53 533 106 53 194 72 34 253 91 28 152 106 38 151 106 53 383 106 0 347 0 34 340 34 34 164 50 18 36 63 31 67 66 34 130 63 31 104 76 18 103 86 18 52 91 23 51 91 28 184 68 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)