# Heptacontagon

Regular heptacontagon
A regular heptacontagon
Type Regular polygon
Edges and vertices 70
Schläfli symbol {70}
t{35}
Coxeter diagram
Symmetry group Dihedral (D70), order 2×70
Internal angle (degrees) ≈174.9°
Dual polygon self
Properties convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a heptacontagon or hebdomecontagon (from Ancient Greek ἑβδομήκοντα, seventy[1]) is a seventy-sided polygon.[2][3] A regular heptacontagon is represented by Schläfli symbol {70} and can be constructed as a quasiregular truncated 35-gon, t{35}, which alternates two types of edges.

The sum of any heptacontagon's interior angles is 12240 degrees.

## Regular heptacontagon properties

One interior angle in a regular heptacontagon is 17467°, meaning that one exterior angle would be 517°.

The area of a regular heptacontagon is (with t = edge length)

$A = \frac{35}{2}t^2 \cot \frac{\pi}{70}$

$r = \frac{1}{2}t \cot \frac{\pi}{70}$

The circumradius of a regular heptacontagon is

$R = \frac{1}{2}t \csc \frac{\pi}{70}$

A regular heptacontagon is not constructible using a compass and straightedge,[4] but is constructible if the use of an angle trisector is allowed.[5]

## Heptacontagram

A heptacontagram is a 70-sided star polygon. There are 11 regular forms given by Schläfli symbols {70/3}, {70/9}, {70/11}, {70/13}, {70/17}, {70/19}, {70/23}, {70/27}, {70/29}, {70/31}, and {70/33}, as well as 23 regular star figures with the same vertex configuration.

 {70/3} {70/9} {70/11} {70/13} {70/17} {70/19} {70/23} {70/27} {70/29} {70/31} {70/33}