Triangle (EntityTopic, 17)
From Hi.gher. Space
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*[[Octahedron]] (8×, 100%) | *[[Octahedron]] (8×, 100%) | ||
*[[Tetrahedron]] (4×, 100%) | *[[Tetrahedron]] (4×, 100%) | ||
| - | *[[ | + | *[[Dodecahedral snub]] (80×, 87%) |
| - | *[[ | + | *[[Cubic snub]] (32×, 84%) |
*[[Square pyramid]] (4×, 80%) | *[[Square pyramid]] (4×, 80%) | ||
*[[Icosidodecahedron]] (20×, 63%) | *[[Icosidodecahedron]] (20×, 63%) | ||
| - | *[[ | + | *[[Dodecahedral truncate]] (20×, 63%) |
*[[Cuboctahedron]] (8×, 57%) | *[[Cuboctahedron]] (8×, 57%) | ||
| - | *[[ | + | *[[Cubic truncate]] (8×, 57%) |
| - | *[[ | + | *[[Tetrahedral truncate]] (4×, 50%) |
*[[Triangular prism]] (2×, 40%) | *[[Triangular prism]] (2×, 40%) | ||
Revision as of 00:14, 23 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.
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 |
