Triangle (EntityTopic, 17)

From Hi.gher. Space

(Difference between revisions)
(polytope explorer integration)
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{{STS Shape
{{STS Shape
| dim=2
| dim=2
-
| elements=3, 3
+
| elements=3 [[digon]]s, 3 [[point]]s
| genus=0
| genus=0
| 20=SSC
| 20=SSC
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}}{{STS Uniform polytope
}}{{STS Uniform polytope
| schlaefli={3}
| schlaefli={3}
 +
| dynkin=x3o
 +
| acronym=Trig, Equit (equilateral), Isot (isosceles)
| vfigure=[[Digon]], length 1
| vfigure=[[Digon]], length 1
| dual=''Self-dual''
| dual=''Self-dual''

Revision as of 16:14, 25 March 2017

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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