### 26.15.9 Checking whether an object in the plane is a rhombus

See Section 27.11.13 for checking for rhombuses in 3D geometry.

The is_rhombus command determines whether or not a geometric object is a rhombus.

- is_rhombus takes G, a geometric object or a sequence of four points assumed to be the vertices of a quadrilateral.
- is_square(G) returns 1 if G is a rhombus but not a square, returns 2 if G is a square and returns 0 otherwise.

#### Examples

is_rhombus(1+i,-1+i,-1-i,1-i)

1 |  |  |  |  |  |  |  |  |  |

K:=rhombus(1+i,-1+i,pi/4); is_rhombus(K)

1 |  |  |  |  |  |  |  |  |  |

K:=rhombus(1+i,-1+i,pi/4,C,D); is_rhombus(K[0])

1 |  |  |  |  |  |  |  |  |  |

Note that K[0] is a rhombus since K is a list made of a rhombus and vertices C and D.

affix(C,D)

−

√

2

−i, −

√

2

+i

is_rhombus(i,-1+i,-1-i,1-i)

0 |  |  |  |  |  |  |  |  |  |