Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:154BQ GHM

Order: 19

Horizontal side: 154 Vertical side: 154

Elements: 2, 2√2, 4, 9√2, 10√2, 11√2, 20, 23, 20√2, 23√2, 27√2, 40, 44, 50, 54, 50√2, 77, 104, 77√2.

Code: 1045 0 50 774 77 77 773 154 77 274 104 50 230 131 77 231 154 77 43 108 50 22 110 52 21 110 54 447 110 54 543 154 0 116 99 41 507 0 50 500 50 50 401 90 50 202 110 30 94 99 41 203 110 10 104 100 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)

104
77√2
77
27√2
23√2
23
4
2√2
2
44
54
11√2
50
50√2
40
20√2
9√2
20
10√2