In
geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a
triskaidecagon (or
tridecagon) is a
polygonIn geometry a polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments . These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners...
with 13 sides and angles.
The measure of each internal angle of a
regularA regular polygon is a polygon which is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
triskaidecagon is approximately 152.308
degreeA degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
s, and the area with side length
a is given by
A regular triskaidecagon is not constructible with
compass and straightedgeCompass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass....
. However, it is constructible using a
Neusis constructionThe neusis is a geometric construction method that was used in antiquity by Greek mathematicians.- Geometric construction :The neusis construction consists of fitting a line element of given length in between two given lines , in such a way that the line element, or its extension, passes through...
.
A triskaidecagram is a 13-sided
star polygonA star polygon is a non-convex polygon which looks in some way like a star. Only the regular ones have been studied in any depth; star polygons in general appear not to have been formally defined...
.
Discussion
Ask a question about 'Triskaidecagon' Start a new discussion about 'Triskaidecagon' Answer questions from other users |
| Regular triskaidecagon |
| 200px |
| Edge In geometry, an edge is a one-dimensional line segment joining two zero-dimensional vertices in a polygon. Thus applied, an edge is a connector for a one-dimensional line segment and two zero-dimensional objects....
s and verticesIn geometry, a vertex is a special kind of point which describes the corners or intersections of geometric shapes. Vertices are commonly used in computer graphics to define the corners of surfaces in 3D models, where each such point is given as a vector.-Of an angle:The vertex of an angle is the...
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13 |
Schläfli symbolIn geometry, the Schläfli symbol is a notation of the form {p,q,r,...} that defines regular polytopes and tessellations.The Schläfli symbol is named after the 19th-century mathematician Ludwig Schläfli who made important contributions in geometry and other areas.- Description :The Schläfli symbol...
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{13} |
| Coxeter–Dynkin diagram |
  |
Symmetry groupThe symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...
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Dihedral (D13) |
AreaArea is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron...
(with t=edge length) |
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| Internal angle In geometry, an interior angle is an angle formed by two sides of a simple polygon that share an endpoint in. This angle must be an angle on the inner side of the polygon to be an internal angle...
(degreeA degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
s) |
180*(11/13) degrees
|
In
geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a
triskaidecagon (or
tridecagon) is a
polygonIn geometry a polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments . These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners...
with 13 sides and angles.
The measure of each internal angle of a
regularA regular polygon is a polygon which is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
triskaidecagon is approximately 152.308
degreeA degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
s, and the area with side length
a is given by
A regular triskaidecagon is not constructible with
compass and straightedgeCompass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass....
. However, it is constructible using a
Neusis constructionThe neusis is a geometric construction method that was used in antiquity by Greek mathematicians.- Geometric construction :The neusis construction consists of fitting a line element of given length in between two given lines , in such a way that the line element, or its extension, passes through...
.
Related polygons
A triskaidecagram is a 13-sided
star polygonA star polygon is a non-convex polygon which looks in some way like a star. Only the regular ones have been studied in any depth; star polygons in general appear not to have been formally defined...
. There are 5 regular forms given by
Schläfli symbolIn geometry, the Schläfli symbol is a notation of the form {p,q,r,...} that defines regular polytopes and tessellations.The Schläfli symbol is named after the 19th-century mathematician Ludwig Schläfli who made important contributions in geometry and other areas.- Description :The Schläfli symbol...
s: {13/2}, {13/3}, {13/4}, {13/5}, {13/6}.