[permalink] [id link]

The regular heptadecagon is the Petrie polygon for one higher-dimensional polytope, projected in a skew orthogonal projection:

from
Wikipedia

## Some Related Sentences

regular and heptadecagon

Gauss was so pleased by this result that he requested that

**a**__regular____heptadecagon__be inscribed on his tombstone.
Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae ( Latin

**,**Arithmetical Investigations ), which**,**among things**,**introduced**the**symbol ≡**for**congruence and used it**in****a**clean presentation of modular arithmetic**,**contained**the**first two proofs of**the**law of quadratic reciprocity**,**developed**the**theories of binary and ternary quadratic forms**,**stated**the**class number problem**for**them**,**and showed that**a**__regular____heptadecagon__( 17-sided**polygon**) can be constructed with straightedge and compass.**The**

__regular__

__heptadecagon__

**is**

**a**constructible

**polygon**( that

**is**

**,**

**one**that can be constructed using

**a**compass and unmarked straightedge ), as was shown by Carl Friedrich Gauss

**in**1796 at

**the**age of 19.

Constructing

**a**__regular____heptadecagon__thus involves finding**the**cosine of**in**terms of square roots**,**which involves an equation of degree 17 —**a**Fermat prime.
** March 30-He obtains conditions

**for****the**constructibility by ruler and compass of__regular__polygons**,**including**the**__heptadecagon__.

regular and is

An extension of 2 months beyond

**the**__regular__due date**for**filing__is__also available to taxpayers making returns**for****a**fiscal year.
But

**for**purely definition purposes -- used**in**conjunction with your__regular__Squatting**,**Leg Curling**,**Leg Extensor programs --**a**heavy weight__is__not needed.
Part-time farming gives

**a**measure of security if**the**__regular__job__is__lost**,**provided**the**farm__is__owned free of debt and furnishes enough income to meet fixed expenses and minimum living costs.
For some white-collar workers it

__is__**a**welcome change from**the**__regular__job**,**and**a**physical conditioner.
A Modest Proposal

__is__**the**name of**The**University of Texas at Dallas ' Alternative Student Newspaper**,****the**monthly opinion paper of**the**University ; it was also**the**name of**a**__regular__column**in**SWIFT Magazine of Harvard University**,****a**satire publication that also takes its name from Jonathan Swift.
For instance

**,****a**local society**in****the**middle of**a**large city may have__regular__meetings with speakers**,**focusing less on observing**the**night sky if**the**membership__is__less able to observe due to factors such as light pollution.
It

__is__common**for**local societies to hold__regular__meetings**,**which may include activities such as star parties or presentations.
In geometry an Archimedean solid

__is__**a**highly symmetric**,**semi-regular convex polyhedron composed of two or more types of__regular__polygons meeting**in**identical vertices.
Since 1995

**the**UK government has advised that__regular__consumption of 3 – 4 units**a**day**for**men**,**or 2 – 3 units**a**day**for**women**,**would not pose significant health risks**,**but that consistently drinking four or more units**a**day ( men ), or three or more units**a**day ( women ),__is__not advisable.
In BrE

**,**both irregular and__regular__forms are current**,**but**for**some words ( such as smelt and leapt ) there__is__**a**strong tendency towards**the**irregular forms**,**especially by users of Received Pronunciation.
A spiritual awakening

__is__achieved by following**the**Twelve Steps**,**and sobriety__is__furthered by volunteering**for**AA and__regular__AA meeting attendance or contact with AA members.
* 959-4444 Manitoba Telephone System ( 204 MB ) ( 959

__is__used as 958__is__**a**__regular__Winnipeg exchange**,**not**a**test prefix )
Phoenix

__is__by far**the**hottest major city**in**North America ;**the**average high temperature during baseball's__regular__season__is__**,**and game-time temperatures well above are very common during**the**summer.**The**term antidepressant

__is__sometimes applied to any therapy ( e. g., psychotherapy

**,**electro-convulsive therapy

**,**acupuncture ) or process ( e. g., sleep disruption

**,**increased light levels

**,**

__regular__exercise ) found to improve

**a**clinically depressed mood.

It

__is__doubtful**,**however**,**that his troops were "__regular__" soldiers**,**but rather**a**hodge-podge of men from various parts of al-Andalus.
After Christians

**in**Ephesus first wrote to their counterparts recommending Apollos to them**,**he went to Achaia where Paul names him as an apostle ( 1 Cor 4**:**6**,**9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15**:**8 ) it__is__certain that Apollos became an apostle**in****the**__regular__way ( as**a**witness to**the**risen Lord and commissioned by Jesus-1 Cor 15**:**5-9 ; 1 Cor 9**:**1 ).< ref > So**the**Alexandrian recension ;**the**text**in**< sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

regular and Petrie

**The**

__regular__icosagon

**is**

**the**

__Petrie__

**polygon**

**for**

**a**number of higher dimensional polytopes

**,**shown

**in**

**orthogonal**projections

**in**Coxeter planes

**:**

**The**

__regular__enneadecagon

**is**

**the**

__Petrie__

**polygon**

**for**

**one**higher dimensional

**polytope**

**,**

**projected**

**in**

**a**

**skew**

**orthogonal**

**projection**

**:**

**The**

__regular__triacontagon

**is**

**the**

__Petrie__

**polygon**

**for**

**a**number of higher dimensional polytopes with E < sub > 8 </ sub > symmetry

**,**shown

**in**

**orthogonal**projections

**in**

**the**E < sub > 8 </ sub > Coxeter plane

**:**

**The**Institute

**is**also responsible

**for**

**the**

__Petrie__Museum of Egyptian Archaeology which

**is**open to

**the**public on

**a**

__regular__basis.

__Petrie__railway station provides access to

__regular__Citytrain services to Brisbane and Ipswich

**,**as well as Caboolture and

**the**Sunshine Coast.

regular and polygon

They are distinct from

**the**Platonic solids**,**which are composed of only**one**type of__polygon__meeting**in**identical vertices**,**and from**the**Johnson solids**,**whose__regular__polygonal faces do not meet**in**identical vertices.
For example

**,****the**perimeter of**a**__regular____polygon__inscribed**in****a**circle approaches**the**circumference with increasing numbers of sides ( and decrease**in****the**length of**one**side ).
While at university

**,**Gauss independently rediscovered several important theorems ; his breakthrough occurred**in**1796 when he showed that any__regular____polygon__with**a**number of sides which**is****a**Fermat prime ( and**,**consequently**,**those polygons with any number of sides which**is****the**product of distinct Fermat primes and**a**power of 2 ) can be constructed by compass and straightedge.**The**wheels can be any

__regular__

__polygon__except

**a**triangle

**,**but

**the**catenary must have parameters corresponding to

**the**shape and dimensions of

**the**wheels.

For example

**,**every__polygon__**is**topologically self-dual ( it has**the**same number of vertices as edges**,**and these are switched by duality ), but will not**in**general be geometrically self-dual ( up to rigid motion**,****for**instance ) –__regular__polygons are geometrically self-dual ( all angles are congruent**,**as are all edges**,**so under duality these congruences swap ), but irregular polygons may not be geometrically self-dual.
In geometry

**,****a**Johnson solid**is****a**strictly convex polyhedron**,**each face of which**is****a**__regular____polygon__**,**but which**is**not uniform**,**i. e., not**a**Platonic solid**,**Archimedean solid**,**prism or antiprism.
Since

**a**__regular____polygon__has angles at least 60 degrees**,**it follows that at most five faces meet at any vertex.
Although there

**is**no obvious restriction that any given__regular____polygon__cannot be**a**face of**a**Johnson solid**,**it turns out that**the**faces of Johnson solids always have 3**,**4**,**5**,**6**,**8**,**or 10 sides.
Any

__polygon__**,**__regular__or irregular**,**self-intersecting or simple**,**has as many corners as it has sides.**The**area of

**a**

__regular__

__polygon__

**is**also given

**in**terms of

**the**radius r of its inscribed circle and its perimeter p by

While it

**is**possible to construct analogies to**the**Penrose triangle with other__regular__polygons to create**a**Penrose__polygon__**,****the**visual effect**is**not as striking**,**and as**the**sides increase**,****the**object seems merely to be warped or twisted.
Carl Friedrich Gauss

**in**1796 showed that**a**__regular__n-sided__polygon__can be constructed with ruler and compass if**the**odd prime factors of n are distinct Fermat primes.
Some

__regular__polygons**,**like**the**heptagon**,**become constructible ; and John H. Conway gives constructions**for**several of them ; but**the**11-sided__polygon__**,****the**hendecagon**,****is**still impossible**,**and infinitely many others.
*

**a**__regular____polygon__that can be constructed with compass and straightedge ; see constructible__polygon__.
In mathematics

**,****a**dihedral group**is****the**group of symmetries of**a**__regular____polygon__**,**including both rotations and reflections.
In this article

**,**D < sub > n </ sub > ( and sometimes Dih < sub > n </ sub >) refers to**the**symmetries of**a**__regular____polygon__with n sides.0.165 seconds.