Square (EntityTopic, 20)
From Hi.gher. Space
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{{Tapertope Nav|2|3|4|2<br>Circle|11<br>Square|1<sup>1</sup><br>Triangle|gons}} | {{Tapertope Nav|2|3|4|2<br>Circle|11<br>Square|1<sup>1</sup><br>Triangle|gons}} | ||
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{{Toratope Nav A||1|2|||II<br>Square|(II)<br>Circle|III<br>Cube|(III)<br>Sphere|gons}} | {{Toratope Nav A||1|2|||II<br>Square|(II)<br>Circle|III<br>Cube|(III)<br>Sphere|gons}} | ||
{{Bracketope Nav|1|2|3|x<br>Digon|[xy]<br>Square|<xy><br>Diamond|gons}} | {{Bracketope Nav|1|2|3|x<br>Digon|[xy]<br>Square|<xy><br>Diamond|gons}} | ||
[[Category:Regular polygons]] | [[Category:Regular polygons]] | ||
Revision as of 16:21, 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 |
| 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. x Digon | 2. [xy] Square | 3. Diamond |
| List of bracketopes | ||
