Triangle (EntityTopic, 17)
From Hi.gher. Space
(Difference between revisions)
m |
(update to STS) |
||
| Line 1: | Line 1: | ||
| - | {{Shape | + | {{STS Shape |
| - | + | ||
| dim=2 | | dim=2 | ||
| elements=3, 3 | | elements=3, 3 | ||
| Line 6: | Line 5: | ||
| 20=SSC | | 20=SSC | ||
| ssc=G3 | | ssc=G3 | ||
| - | |||
| - | |||
| pv_circle=<sup>[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>π</sub> ≈ 0.2757 | | pv_circle=<sup>[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>π</sub> ≈ 0.2757 | ||
| pv_square=[[Sine values|S<sub>1</sub>]]+S<sub>1</sub><sup>3</sup>S<sub>5</sub><sup>-2</sup> ≈ 0.2774 | | pv_square=[[Sine values|S<sub>1</sub>]]+S<sub>1</sub><sup>3</sup>S<sub>5</sub><sup>-2</sup> ≈ 0.2774 | ||
| + | | extra={{STS Rotope | ||
| + | | attrib=pure | ||
| + | | notation=1<sup>1</sup> x<sup>y</sup> | ||
| + | | index=3 | ||
| + | }}{{STS Uniform polytope | ||
| schlaefli={3} | | schlaefli={3} | ||
| vfigure=[[Line segment]], length 1 | | vfigure=[[Line segment]], length 1 | ||
| dual=''Self-dual'' | | dual=''Self-dual'' | ||
| - | }} | + | }}}} |
A '''triangle''' is a two-dimensional [[simplex]]. | A '''triangle''' is a two-dimensional [[simplex]]. | ||
Revision as of 08:44, 14 March 2008
A triangle is a two-dimensional simplex.
The triangle is important as all polygons can be defined as the union of a set of triangles, and all polytopes in greater than two dimensions can be defined as the hypervolume bounded by the union of a set of triangles.
Equations
- The area of an arbitrary triangle is:
absin(C)2-1
- where a and b are two sides of the triangle and C is the angle between them.
Segmentation
The equilateral triangle of side 1 may be segmented into 3× triangle with sides 1, 2×3-2-1 and angles 2×30°, 120°.
Use
Triangular faces are found in these trishapes on FGwiki:
- Icosahedron (20×, 100%)
- Octahedron (8×, 100%)
- Tetrahedron (4×, 100%)
- Dodecahedral snub (80×, 87%)
- Cubic snub (32×, 84%)
- Square pyramid (4×, 80%)
- Icosidodecahedron (20×, 63%)
- Dodecahedral truncate (20×, 63%)
- Cuboctahedron (8×, 57%)
- Cubic truncate (8×, 57%)
- Tetrahedral truncate (4×, 50%)
- Triangular prism (2×, 40%)
Triangular segments are found in these dishapes on FGwiki:
- Hexagon (6×)
| Notable Dishapes | |
| Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
| Curved: | circle |
