Triangle (EntityTopic, 17)
From Hi.gher. Space
(Difference between revisions)
m |
(add) |
||
| Line 13: | Line 13: | ||
== Segmentation == | == Segmentation == | ||
The equilateral triangle of side 1 may be [[segment]]ed into 3× triangle with sides 1, 2×3<sup>-2<sup>-1</sup></sup> and angles 2×30°, 120°. | The equilateral triangle of side 1 may be [[segment]]ed into 3× triangle with sides 1, 2×3<sup>-2<sup>-1</sup></sup> and angles 2×30°, 120°. | ||
| + | |||
| + | == Use == | ||
| + | Triangular faces are found in these [[polyhedra]] on FGwiki: | ||
| + | *[[Icosahedron]] (20×, 100%) | ||
| + | *[[Octahedron]] (8×, 100%) | ||
| + | *[[Tetrahedron]] (4×, 100%) | ||
| + | *[[Square pyramid]] (4×, 80%) | ||
| + | *[[Truncated cube]] (8×, 57%) | ||
| + | *[[Truncated tetrahedron]] (4×, 50%) | ||
| + | *[[Triangular prism]] (2×, 40%) | ||
| + | *[[Truncated dodecahedron]] (20×, 63%) | ||
| + | *[[Snub cube]] (32×, 84%) | ||
| + | *[[Snub dodecahedron]] (80×, 87%) | ||
| + | *[[Cuboctahedron]] (8×, 57%) | ||
| + | |||
| + | These [[polygon]]s on FGwiki can be segmented into triangles: | ||
| + | *[[Hexagon]] (6×) | ||
{{Dishapes}} | {{Dishapes}} | ||
{{Rotope Nav|2|3|4|II<br>Square|I'<br>Triangle|(II)<br>Circle|gons}} | {{Rotope Nav|2|3|4|II<br>Square|I'<br>Triangle|(II)<br>Circle|gons}} | ||
[[Category:Regular polygons]] | [[Category:Regular polygons]] | ||
Revision as of 11:04, 22 September 2007
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.
Geometry
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 polyhedra on FGwiki:
- Icosahedron (20×, 100%)
- Octahedron (8×, 100%)
- Tetrahedron (4×, 100%)
- Square pyramid (4×, 80%)
- Truncated cube (8×, 57%)
- Truncated tetrahedron (4×, 50%)
- Triangular prism (2×, 40%)
- Truncated dodecahedron (20×, 63%)
- Snub cube (32×, 84%)
- Snub dodecahedron (80×, 87%)
- Cuboctahedron (8×, 57%)
These polygons on FGwiki can be segmented into triangles:
- Hexagon (6×)
| Notable Dishapes | |
| Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
| Curved: | circle |
