Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:220DC GHM

Order: 19

Horizontal side: 220 Vertical side: 220

Elements: 2, 2√2, 4, 3√2, 6, 7√2, 20, 20√2, 40, 30√2, 40√2, 70, 74, 76, 80, 70√2, 74√2, 146, 110√2.

Code: 1465 0 74 1104 110 110 803 220 140 306 110 110 405 140 100 404 180 100 706 150 70 205 140 80 204 160 80 61 146 80 45 146 76 74 153 73 25 146 74 24 148 74 763 150 0 32 153 73 745 0 0 744 74 0 705 150 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)

146
110√2
80
30√2
40
40√2
70√2
20
20√2
6
4
7√2
2
2√2
76
3√2
74
74√2
70