### 27.6.4 Equilateral triangles in space

See Section 26.7.4 for equilateral triangles in the plane.

The equilateral_triangle command returns and draws equilateral triangles.

- equilateral_triangle takes three mandatory arguments and one optional argument:
  - A,B,P, three points.
  - Optionally, var, a variable name.
- equilateral_triangle(A,B,P ⟨,var⟩) returns and draws equilateral triangle ABC, where C and P are on the same side of line AB in plane ABP.

  If the argument var is given, it will be assigned the value of C.

#### Examples

A,B,p:=point(0,0,0),point(3,3,3),point(0,0,3); equilateral_triangle(A,B,P)

A,B,P:=point(0,0,0),point(3,3,3),point(0,0,3); equilateral_triangle(A,B,P,C); simplify(coordinates(C))

| ⎡ ⎢ ⎢ ⎣ |
−3 | √ |
6
| +6
4
| , |
−3 | √ |
6
| +6
4
| , |
3 | √ |
6
| +3
2
| ⎤ ⎥ ⎥ ⎦