Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:212AY1of4 GHM

Order: 19

Horizontal side: 212 Vertical side: 212

Elements: 4, 4√2, 8, 8√2, 12, 14, 12√2, 13√2, 14√2, 26, 26√2, 40, 53√2, 80, 66√2, 106, 80√2, 132, 106√2.

Code: 1325 0 80 1064 106 106 1063 212 106 264 132 80 140 158 106 141 172 106 407 172 106 536 159 53 40 144 92 41 148 92 125 148 80 124 160 80 263 172 66 80 140 88 81 148 88 805 0 0 804 80 0 660 146 66 134 159 53

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)

132
106√2
106
26√2
14√2
14
40
53√2
4√2
4
12
12√2
26
8√2
8
80
80√2
66√2
13√2