Square (EntityTopic, 20)
From Higher Dimensions Database
A square is a two-dimensional hypercube.
l ⇒ length of edges of the square
- The radial slices θ of a square are:
[:x,:y] ⇒ digon of length lsin(45° + (θ % 90°)√2
Any unstated homology group is the trivial group 0.
- 0-frame (four points)
- H0 = 4ℤ
- 1-frame (four line segments)
- H0 = ℤ, H1 = ℤ
- 2-frame (solid square)
- H0 = ℤ
A diamond is the dual of a square when orientation is preserved. In other words, it's a square rotated around the origin by 45 degrees.
The diamond should not be confused with the rhombus.
The diamond is a brick with unique points at (1,0) and (0,1). It represents the tegum product and the SUM function.
The square is a brick with one unique point at (1,1). It represents the Cartesian product and the MAX function.
Square faces are found in these trishapes on FGwiki:
- Cube (6×, 100%)
- Triangular prism (3×, 60%)
- Cuboctahedron (6×, 43%)
- Octahedral truncate (6×, 43%)
- Square antiprism (2×, 20%)
- Square pyramid (1×, 20%)
- Cubic snub (6×, 16%)
|point • digon • square • cube • geochoron • geoteron • geopeton|
|Flat:||triangle • square • pentagon • hexagon • octagon • decagon|
|List of tapertopes|
|List of toratopes|
|List of bracketopes|