Triangle (EntityTopic, 17)

From Hi.gher. Space

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A '''triangle''' is a two-dimensional [[simplex]].
A '''triangle''' is a two-dimensional [[simplex]].
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The equilateral triangle of side 1 may be [[dissect]]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 [[dissect]]ed into 3× triangle with sides 1, 2×3<sup>-2<sup>-1</sup></sup> and angles 2×30°, 120°.
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== Use ==
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<[#polytope [id -3]]>
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Triangular faces are found in these trishapes on FGwiki:
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*[[Icosahedron]] (20×, 100%)
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*[[Octahedron]] (8×, 100%)
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*[[Tetrahedron]] (4×, 100%)
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*[[Dodecahedral snub]] (80×, 87%)
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*[[Cubic snub]] (32×, 84%)
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*[[Square pyramid]] (4×, 80%)
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*[[Icosidodecahedron]] (20×, 63%)
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*[[Dodecahedral truncate]] (20×, 63%)
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*[[Cuboctahedron]] (8×, 57%)
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*[[Cubic truncate]] (8×, 57%)
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*[[Tetrahedral truncate]] (4×, 50%)
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*[[Triangular prism]] (2×, 40%)
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Triangular segments are found in these dishapes on FGwiki:
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*[[Hexagon]] (6×)
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{{Simplices|2}}
{{Simplices|2}}
{{Dishapes}}
{{Dishapes}}
{{Tapertope Nav|3|4|5|11<br>Square|1<sup>1</sup><br>Triangle|3<br>Sphere|gons}}
{{Tapertope Nav|3|4|5|11<br>Square|1<sup>1</sup><br>Triangle|3<br>Sphere|gons}}

Revision as of 22:01, 16 February 2014

A triangle is a two-dimensional simplex.

Equations

  • The area of an equilateral triangle with side length l is:
√3∕4 · l2
  • The area of an arbitrary triangle, where a and b are two sides of the triangle and C is the angle between them, is:
1∕2 · ab · sin C

Dissection

The equilateral triangle of side 1 may be dissected into 3× triangle with sides 1, 2×3-2-1 and angles 2×30°, 120°.

Incidence matrix

Dual: Self-dual

#TXIDVaEaTypeName
0 Va= point ;
1 Ea2= digon ;
2 3a33= triangle ;

Usage as facets


Simplices
triangle • tetrahedron • pyrochoron • pyroteron • pyropeton


Notable Dishapes
Flat: triangle • square • pentagon • hexagon • octagon • decagon
Curved: circle


3. 11
Square 		4. 11
Triangle 		5. 3
Sphere
List of tapertopes
Retrieved from "http://hi.gher.space/wiki/Triangle"

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