Square (EntityTopic, 20)
From Hi.gher. Space
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(Added homology groups. This might look better as a table. Also how do I get blackboard bold and the circle plus in this wiki?) |
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*The [[radial slice]]s ''θ'' of a square are: | *The [[radial slice]]s ''θ'' of a square are: | ||
<blockquote>[:x,:y] ⇒ [[digon]] of length ''l''sin(45° + (''θ'' % 90°)√2</blockquote> | <blockquote>[:x,:y] ⇒ [[digon]] of length ''l''sin(45° + (''θ'' % 90°)√2</blockquote> | ||
| + | |||
| + | == Homology Groups == | ||
| + | Any unstated homology group is the trivial group 0. | ||
| + | |||
| + | 0-frame (four points): | ||
| + | H<sub>0</sub> = 4Z | ||
| + | |||
| + | 1-frame (four line segments): | ||
| + | H<sub>0</sub> = Z | ||
| + | H<sub>1</sub> = Z | ||
| + | |||
| + | 2-frame (solid square): | ||
| + | H<sub>0</sub> = Z | ||
| + | |||
== Brick == | == Brick == | ||
Revision as of 07:36, 24 November 2009
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
Brick
The square is a brick with one unique point at (1,1). It represents the Cartesian product and the MAX function.
Segmentation
The square of side 2 may be segmented 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 |
| 1. x Digon | 2. [xy] Square | 3. Diamond |
| List of bracketopes | ||
