Rank2
TypeRegular
Notation
Coxeter diagramx42o ()
Schläfli symbol{42}
Elements
Edges42
Vertices42
Vertex figureDyad, length ${\displaystyle 2\cos(\pi /42)}$
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1}{2\sin \left({\frac {\pi }{42}}\right)}}\approx 6.690745}$
Inradius${\displaystyle {\frac {1}{2\tan \left({\frac {\pi }{42}}\right)}}\approx 6.67204}$
Area${\displaystyle {\frac {21}{2\tan \left({\frac {\pi }{42}}\right)}}\approx 140.11276}$
Angle${\displaystyle {\frac {20\pi }{21}}\approx 342.85714^{\circ }}$
Central density1
Related polytopes
Abstract & topological properties
Flag count84
Euler characteristic0
OrientableYes
Properties
SymmetryI2(42), order 84
Flag orbits1
ConvexYes
Net count1
NatureTame

The tetracontadigon is a regular polygon with 42 sides. A regular tetracontadigon has equal sides and equal angles.

It is the largest finite convex regular polygon that can be used in a planar vertex, although no regular faced tiling of the plane includes a tetracontadigon.