Square (EntityTopic, 20)

From Hi.gher. Space

Revision as of 16:21, 24 November 2009 by Hayate (Talk | contribs)


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
[: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:

See also


Hypercubes
pointdigonsquarecubegeochorongeoterongeopeton


Notable Dishapes
Flat: trianglesquarepentagonhexagonoctagondecagon
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

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