Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:172BT GHM

Order: 19

Horizontal side: 172 Vertical side: 172

Elements: 1√2, 2, 2√2, 3√2, 4√2, 7√2, 14, 28, 24√2, 34, 38, 48, 38√2, 62, 48√2, 55√2, 62√2, 110, 86√2.

Code: 1105 0 62 864 86 86 386 134 134 483 134 86 385 134 96 25 134 94 24 136 94 36 135 93 347 138 96 486 124 48 42 138 90 14 135 93 283 138 62 244 110 62 625 0 0 624 62 0 76 117 55 147 124 62 550 117 55

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)

110
86√2
38√2
48
38
2
2√2
3√2
34
48√2
4√2
1√2
28
24√2
62
62√2
7√2
14
55√2