Square (EntityTopic, 20)

From Hi.gher. Space

(Difference between revisions)
m (add SSC3)
m (Undo revision 6731 by Hayate (talk) premature)
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| ssc=[xy] or G4
| ssc=[xy] or G4
| ssc2=G4
| ssc2=G4
-
| ssc3=<2, 4>
 
| pv_circle=<sup>2</sup>⁄<sub>π</sub> ≈ 0.6366
| pv_circle=<sup>2</sup>⁄<sub>π</sub> ≈ 0.6366
| pv_square=1
| pv_square=1

Revision as of 16:34, 22 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
[: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:

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. I
Digon
2. [II]
Square
3. (II)
Circle
List of bracketopes

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