# Triangle (EntityTopic, 17)

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

 # TXID Type Name Va Ea 0 Va = point ; 1 Ea 2 = digon ; 2 3a 3 3 = triangle ;

## Usage as facets

 Simplices triangle • tetrahedron • pyrochoron • pyroteron • pyropeton

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

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

## Pages in this category (1)

 Triangular prism