A **triangle** is the 2-simplex. The study of triangles is called trigonometry (plus the study of angles). Its Bowers acronym is "**trig**". It is also known as a **pyrogon** under the elemental naming scheme.

## Types of Triangle

### By Sides

#### Equilateral

When all of the angles and edges of a triangle are equal a triangle is equilateral. Each angle must have a measure of exactly 60 degrees.

#### Isosceles

When a triangle has two equal sides, it is isosceles. It must also have two equal angles.

#### Scalene

A triangle with three unique side lengths is known as a scalene triangle.

### By Angles

#### Acute

A triangle with all three angles smaller than 90 degrees is called an acute triangle. All equilateral triangles are also acute triangles.

#### Right-Angled

A triangle with one right angle is a right-angled triangle. Their side lengths follow the equation , where c is the edge length of the side opposite the right angle.

#### Obtuse

A triangle where at least one angle is greater than 90 degrees is called an obtuse triangle.

### Special Cases

A triangle with more than one right angle is usually degenerate, but can appear on the surface of a sphere. The same applies to a triangle with angles that sum to greater than 180 degrees, and to triangles that have any angle equal to 180 degrees.

## Structure and Sections

### Hypervolumes

### Subfacets

- 3 points (0D)
- 3 line segments (1D)
- 1
**triangle**(2D)

## See Also

Zeroth | First | Second | Third | Fourth | Fifth | Sixth | Seventh | Eighth | Ninth | Tenth | Eleventh | Twelfth | Thirteenth | Fourteenth | Fifteenth | Sixteenth | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Simplex | Point | Line segment | Triangle
| Tetrahedron | Pentachoron | Hexateron | Heptapeton | Octaexon | Enneazetton | Decayotton | Hendecaxennon | Dodecadakon | Tridecahendon | Tetradecadokon | Pentadecatradakon | Hexadecatedakon | Heptdecapedakon |

Hypercube | Point | Line segment | Square | Cube | Tesseract | Penteract | Hexeract | Hepteract | Octeract | Enneract | Dekeract | Hendekeract | Dodekeract | Tridekeract | Tetradekeract | Pentadekeract | Hexadekeract |

Cross | Point | Line segment | Square | Octahedron | Hexadecachoron | Pentacross | Hexacross | Heptacross | Octacross | Enneacross | Dekacross | Hendekacross | Dodekacross | Tridekacross | Tetradekacross | Pentadekacross | Hexadekacross |

Hypersphere | Point | Line segment | Disk | Ball | Gongol | Pentorb | Hexorb | Heptorb | Octorb | Enneorb | Dekorb | Hendekorb | Dodekorb | Tridekorb | Tetradekorb | Pentadekorb | Hexadekorb |

... | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Monogon | Digon | Triangle
| Square | Pentagon | Hexagon | Heptagon | Octagon | Enneagon | Decagon | ... | Apeirogon |

Regular | Rectified | Truncated |
---|---|---|

Triangle
| Triangle
| Hexagon |