The snub square tiling can be constructed as a snub operation from the square tiling, or as an alternate truncation from the truncated square tiling.
An alternate truncation deletes every other vertex, creating a new triangular faces at the removed vertices, and reduces the original faces to half as many sides. In this case starting with a truncated square tiling with 2 octagons and 1 square per vertex, the octagon faces into squares, and the square faces degenerate into edges and 2 new triangles appear at the truncated vertices around the original square.
If the original tiling is made of regular faces the new triangles will be isosceles. Starting with octagons which alternate long and short edge lengths will produce a snub tiling with perfect equilateral triangle faces.
Example:
Regular octagons alternately truncated |
→
(Alternate truncation) |
Isosceles triangles (Nonuniform tiling) |
Nonregular octagons alternately truncated |
→
(Alternate truncation) |
Equilateral triangles |
Read more about Snub Square Tiling: Related Tilings, Circle Packing, See Also
Famous quotes containing the words snub and/or square:
“Odysseus saw the sirens; they were charming,
Blonde, with snub breasts and little neat posteriors,”
—John Streeter Manifold (b. 1915)
“The square dance fiddler’s first concern is to carry a tune, but he must carry it loud enough to be heard over the noise of stamping feet, the cries of the “caller,” and the shouts of the dancers. When he fiddles, he “fiddles all over”; feet, hands, knees, head, and eyes are all busy.”
—State of Oklahoma, U.S. public relief program (1935-1943)