Triangle (EntityTopic, 17)

From Hi.gher. Space

A triangle is a two-dimensional simplex.

Triangles are one of the three regular polygons that can tile the plain, forming the triangular tiling.

Coordinates

The Cartesian coordinates of an equilateral triangle centered at the origin with side length 2 are:

(-1, -√3/3), (1, -√3/3), (0, 2√3/3)

Equations

  • The area of an equilateral triangle with side length l is:
√34 · l2
  • The area of an arbitrary triangle, where a and b are two sides of the triangle and C is the angle between them, is:
12 · ab · sin C

Dissection

The equilateral triangle of side 1 may be dissected into 3× triangle with sides 1, √3/3, √3/3 and angles 30°, 30°, 120°.

Incidence matrix

Dual: Self-dual

#TXIDVaEaTypeName
0 Va= point ;
1 Ea2= digon ;
2 3a33= triangle ;

Usage as facets


Simplices
triangletetrahedronpyrochoronpyroteronpyropeton


Notable Dishapes
Flat: trianglesquarepentagonhexagonoctagondecagon
Curved: circle


3. 11
Square
4. 11
Triangle
5. 3
Sphere
List of tapertopes

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