„Hétszög” változatai közötti eltérés

!bgcolor=#e7dcc3 colspan=2|Szabályos hétszög

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|bgcolor=#e7dcc3|[[Él]]ek és [[csúcs]]ok||7

|bgcolor=#e7dcc3|[[Schläfli szimbólum]]||{7}

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|bgcolor=#e7dcc3|[[Szimmetriacsoport]]||[[Diéderes]] (D₇)

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== Szerkesztés ==

A regular heptagon is not [[Constructible polygon|constructible]] with [[compass and straightedge]] but is constructible with a marked [[ruler]] and compass. This type of construction is called a [[Neusis construction]]. It is also constructible with compass, straightedge and angle

trisector. The impossibility of straightedge and compass construction follows from the observation that 2cos(2π/7) ≈ 1.247 is a zero of the [[irreducible polynomial|irreducible]] [[cubic function|cubic]] ''x''³ + ''x''² – 2''x'' – 1. Consequently this polynomial is the [[minimal polynomial]] of 2cos(2π/7), whereas the degree of the minimal polynomial for a [[constructible number]] must be a power of 2.