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Octadecagon

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Regular octadecagon

Edge Edge (geometry) 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 vertices Vertex (geometry) In 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...	18
Schläfli symbol Schläfli symbol In 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...	{18} t{9}
Coxeter–Dynkin diagram
Symmetry group Symmetry group The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...	Dihedral (D₁₈)
Area Area Area 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)
Internal angle 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... (degree Degree (angle) A 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)	160°

An octadecagon is a polygon

Polygon

In 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 18 sides

Edge (geometry)

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....

and 18 vertices

Vertex (geometry)

In 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...

. Another name for an octadecagon is octakaidecagon.

Petrie polygons

The regular octadecagon

Octadecagon

An octadecagon is a polygon with 18 sides and 18 vertices. Another name for an octadecagon is octakaidecagon.- Petrie polygons :The regular octadecagon is the Petrie polygon for seven higher dimensional polytopes, shown in these skew orthogonal projections:...

is the Petrie polygon

Petrie polygon

In geometry, a Petrie polygon of a regular polygon is the regular polygon itself. The Petrie polygon of a regular polyhedron is a skew polygon such that every two consecutive sides belong to a face of a regular polyhedron...

for seven higher dimensional polytopes, shown in these skew orthogonal projections:

9-orthoplex (9D)	9-cube (9D)	10-demicube 10-demicube In geometry, a demidekeract or 10-demicube is a uniform 10-polytope, constructed from the 10-cube with alternated vertices deleted. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.... (10D)
3₂₁ polytope (7D)	2₃₁ polytope Gosset 2 31 polytope In 7-dimensional geometry, 2₃₁ is a uniform polytope, constructed from the E7 group. It is named by Coxeter as 2₃₁ by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node sequence.... (7D)	1₃₂ polytope Gosset 1 32 polytope In 7-dimensional geometry, 1₃₂ is a uniform polytope, constructed from the E7 group. It is named by Coxeter as 1₃₂ by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node sequence.... (7D)
17-simplex (11D)