As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge): this was shown by Carl Friedrich Gauss in 1796 at the age of 19.

[1] This proof represented the first progress in regular polygon construction in over 2000 years.

[1] Gauss's proof relies firstly on the fact that constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions, and secondly on his proof that this can be done if the odd prime factors of

, the number of sides of the regular polygon, are distinct Fermat primes, which are of the form

Constructing a regular heptadecagon thus involves finding the cosine of

Gauss's book Disquisitiones Arithmeticae[2] gives this (in modern notation) as[3] Constructions for the regular triangle, pentagon, pentadecagon, and polygons with 2h times as many sides had been given by Euclid, but constructions based on the Fermat primes other than 3 and 5 were unknown to the ancients.

The explicit construction of a heptadecagon was given by Herbert William Richmond in 1893.

Another construction of the regular heptadecagon using straightedge and compass is the following: T. P. Stowell of Rochester, N. Y., responded to Query, by W.E.

Heal, Wheeling, Indiana in The Analyst in the year 1877:[5] "To construct a regular polygon of seventeen sides in a circle.

Draw the radius CO at right-angles to the diameter AB: On OC and OB, take OQ equal to the half, and OD equal to the eighth part of the radius: Make DE and DF each equal to DQ and EG and FH respectively equal to EQ and FQ; take OK a mean proportional between OH and OQ, and through K, draw KM parallel to AB, meeting the semicircle described on OG in M; draw MN parallel to OC, cutting the given circle in N – the arc AN is the seventeenth part of the whole circumference."

Therefore, applying induction with m=1 and starting with n=0: The regular heptadecagon has Dih17 symmetry, order 34.

Cyclic symmetries in the middle column are labeled as g for their central gyration orders.

Since 17 is a prime number, all of these are regular stars and not compound figures.