Triangle (EntityTopic, 17)

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A triangle is a two-dimensional simplex.

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

Equations

  • The area of an equilateral triangle with side length l is:
√3∕4 · 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:
1∕2 · 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
triangle • tetrahedron • pyrochoron • pyroteron • pyropeton


Notable Dishapes
Flat: triangle • square • pentagon • hexagon • octagon • decagon
Curved: circle


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