Triacontagon

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Triacontagon
Rank2
TypeRegular
Notation
Coxeter diagramx30o ()
Schläfli symbol{30}
Elements
Edges30
Vertices30
Vertex figureDyad, length
Measures (edge length 1)
Circumradius
Inradius
Area
Angle
Central density1
Number of external pieces30
Level of complexity1
Related polytopes
DualTriacontagon
Conjugate3 total
Abstract & topological properties
Flag count60
Euler characteristic0
OrientableYes
Properties
SymmetryI2(30), order 60
Flag orbits1
ConvexYes
NatureTame

The triacontagon is a polygon with 30 sides. A regular triacontagon has equal sides and equal angles.

This polygon is notable for the property that there exist sets of 7 diagonals, all concurrent in a point other than the center. No other regular polygon has more concurrent diagonals, and any other polygon with this property must have a multiple of 30 sides.[1]

Since 30 = 2 × 3 × 5 is the product of different Fermat primes, a regular triacontagon is constructible with straightedge and compass.

Gallery[edit | edit source]

External links[edit | edit source]

References[edit | edit source]

  1. Poonen, Bjorn; Rubinstein, Michael (1995), The Number of Intersection Points Made by the Diagonals of a Regular Polygon