Square (EntityTopic, 20)
From Hi.gher. Space
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The square is a brick with one unique point at (1,1). It represents the [[Cartesian product]] and the MAX function. | The square is a brick with one unique point at (1,1). It represents the [[Cartesian product]] and the MAX function. | ||
| - | == | + | == Dissection == |
| - | The square of side 2 may be [[ | + | The square of side 2 may be [[dissect]]ed into 4× [[triangle]] with sides 2, 2×2<sup>2<sup>-1</sup></sup> and angles 2×45°, 90°. |
== Use == | == Use == | ||
Revision as of 15:07, 21 November 2011
A square is a two-dimensional hypercube.
Squares are the most common base for two-dimensional manifolds and polyominoes.
Equations
- Variables:
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
Homology groups
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
Diamond
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.
Brick
The diamond is a brick with unique points at (1,0) and (0,1). It represents the tegum product and the SUM function.
Brick
The square is a brick with one unique point at (1,1). It represents the Cartesian product and the MAX function.
Dissection
The square of side 2 may be dissected into 4× triangle with sides 2, 2×22-1 and angles 2×45°, 90°.
Use
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%)
See also
| Hypercubes |
| point • digon • square • cube • geochoron • geoteron • geopeton |
| Notable Dishapes | |
| Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
| Curved: | circle |
| 2. 2 Circle | 3. 11 Square | 4. 11 Triangle |
| List of tapertopes | ||
| a. | b. | 1a. II Square | 1b. (II) Circle | 2a. III Cube | 2b. (III) Sphere |
| List of toratopes | |||||
| 1. I Digon | 2. [II] Square | 3. (II) Circle |
| List of bracketopes | ||
