Wythoff Constructions From Square Tiling
Like the uniform polyhedra there are eight uniform tilings that can be based from the regular square tiling.
Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, all 8 forms are distinct. However treating faces identically, there are only three topologically distinct forms: square tiling, truncated square tiling, snub square tiling.
| Symmetry:, (*442) | +, (442) | , (4*2) | ||||||
|---|---|---|---|---|---|---|---|---|
| t0{4,4} | t0,1{4,4} | t1{4,4} | t1,2{4,4} | t2{4,4} | t0,2{4,4} | t0,1,2{4,4} | s{4,4} | h0,1{4,4} |
| Uniform duals | ||||||||
| V4.4.4.4 | V4.8.8 | V4.4.4.4 | V4.8.8 | V4.4.4.4 | V4.4.4.4 | V4.8.8 | V3.3.4.3.4 | |
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Famous quotes containing the word square:
“If the physicians had not their cassocks and their mules, if the doctors had not their square caps and their robes four times too wide, they would never had duped the world, which cannot resist so original an appearance.”
—Blaise Pascal (1623–1662)