5 - 6 - 7
Why stars of the sheriffs have five, six and seven points?
Skol'ko luchey ispuskaet zvezda sherifa?

Tak na vopros o zvezdah otvechali amerikancy:

James T. Dunnam
  I will check on the points to the Sheriff's Star.
  Voz'mu etot vopros pod svoy kontrol'!

Mike (Zeke) Doro
Warren County Kentucky, USA

http://wcdare.com
  I tried to find the answer to your question about the sheriff's badge. It seems that the original design of the star was meant to give hope. It was an inspiritational design of a shining star of hope. Where it first originated is a mystery but it was copied and transformed many times. The number of points may have many different meanings. It may represent a date or just the designers artistic feelings.
  Dumaiu, chto original'nyy proekt byl simvolom voodushevliaiushey zvezdy nadezhdy. Gde on voznik - tayna. Kolichestvo luchey mozhet imet' raznyy smysl. Naprimer, byt' sviazan s kakoy-libo datoy ili otvechat' hudozhestvennomu vkusu razrabotchikov.

Brian J. McLean
Sheriff, Houghton County
http://www.houghtonsheriff.com
  That is a very good observation, and yes, you are correct. Here in Michigan all of the Sheriffs use a six-point star. In Texas, they use the five point star, and in the South (Florida, South Carolina, etc.) the seven point star is most common. Sorry to say I do not know why there is a difference, I think it's just a matter of chance.
  Da, vopros postavlen verno. Zdes', v Michigane, u vseh sherifov shestiluchevye zvezdy. V Tehase zvezdy piatikonechnye, a na Iuge (Florida, IUzhnaia Karolina i t.p.) chashe vsego ispol'zuiutsia semikonechnye. Navernoe, eto prosto delo sluchaia.

Vince Delgato
  No special reason for amount of points.
  Ne bylo nikakoy osoboy prichiny dlia kolichestva luchey, naprimer, dlia shest' vybrali potomu, chto sochli eto bolee krasivym.

Robert Marino
  I don't have any idea why a sheriffs star has a certain number of rays, any more than I know what is the meaning of life (it does have one doesn't it?)
  Mne kazhetsia, chto eto sviazano so smyslom zhizni...

The Handbook of Texas Online
http://www.tsha.utexas.edu/handbook/online/articles/view/FF/msf1.html
FLAGS OF TEXAS.
  The "Zavala flag" was allegedly adopted in Convention of 1836qv at Washington-on-the-Brazos. It is usually portrayed as a blue field with a white star of five points central and with the letters "TEXAS," one letter at each star point....In addition, the actual configuration of the flag is unknown because the journal does not describe Zavala's proposal of March 11, 1836, though it does state that William B. Scates'sqv motion to add a "Rainbow and star of five points above the western horizon; and a star of six points sinking below" was accepted. Finally, the journal reflects that Charles Stanfield Taylor,qv not Zavala, suggested that the letters "TEXAS" be placed around the star....The most commonly known Confederate battle flag was the flag used by the Army of Northern Virginia. It was a square having a red ground with a blue saltire bordered with white and emblazoned with white five-pointed stars corresponding in number to that of the Confederate States.
  Iz istorii flaga shtata Tehas izvestno, chto delalis' popytki razmestit' naimenovanie shtata v luchah zvezdy, chto i potrebovalo piatikonechnoy zvezdy.

Racine County Sheriff's Department, Wisconsin
http://www.racineco.com/sheriff/gang8.htm
STARS
  The five pointed star is a symbol of the People Nation and the six pointed star (the Jewish Star of David) is a symbol of the Folks Nation
  Eto mozhno poniat' tak: piatikonechnaia zvezda - simvol amerikanskogo naroda, a shestikonechnaia zvezda Davida - simvol evreyskogo Naroda Biblii. I ob'iasnenie zvezdy, kak gruppovoy simvoliki daetsia na sayte sherifa!

EquiHex™Designs
http://www.equihex.com/meanings.htm
5-point star
  The five-pointed star, when portrayed with crossed lines, is called a pentagram. When the pentagram is drawn with two points up it is said to be a symbol of devil worship: the two points at the top supposedly symbolizing the horns of the devil. In the past, however, the pentagram was used by the Norse as a symbol of protection from evil and as a symbol called the "Seal of Solomon" in Jewish mysticism. Today 5-pointed stars are used as a symbol of merit, of a job done well (as on papers in grade school) or as a symbol of excellence (as in movie and restaurant ratings), on sheriff's badges, flags and by the military of many countries. In current hex sign mythology, the 5-pointed star is purported to be a symbol of protection from fire and lightning or a protection for livestock, a meaning closely related to the use of these stars by ancient Norsemen. In general, the 5-pointed star, displayed with one point at the top, is considered lucky..
  V proshlom piatikonechnuiu zvezdu sviazyvali s d'iavolom, nazyvaia ee "pechat'iu Solomona". Segodnia ee smysl izmenilsia i oznachaet kachestvo, uspeh, sovershenstvo. V shestnadcatirichnoy mifologii - simvol zashity ot ognia i molnii.

Online version of Carl G Liungman's book Thought Signs (IOS Press, ISBN 90 5199 197 5)
http://www.symbols.com/encyclopedia/30/3059.html
  An Egyptian hieroglyph used in expressions meaning the underworld or the kingdom of death. The fivepointed star inside the circle is an Egyptian hieroglyph meaning star.
  V egipetskoy ieroglifike piatikonechnaia zvezda simvolizirovala prestupnyy mir ili korolevstvo smerti.

Wendy I Valdez
  I wondered why as well. I wasn't able to find an exact answer, but did find this website on a general history of badges and stars worn by police officers: www.texasranger.org/HFM/TinStar.htm
  Horoshiy sovet obratit'sia k opytnym liudiam.

Frank W. Latham
Late Chief of Police
Hewitt, Texas Police Department

http://www.texasranger.org/HFM/TinStar.htm
  Furthermore, many officers and some agencies, still like badges that help reflect their rich frontier heritage and tradition. The Texas Rangers are issued a five point star with a circle around it, made from Mexican silver five-peso coin (still visible on the back of the badge). The Louisiana State Police use a badge shaped like their state, as does Mississippi. The oldest federal law enforcement agency, the U.S. Marshals Service have gone back to a large five-point ball-tipped star, surrounded by a circle, with an eagle in the center, as their "new" badge.
  Many agencies have rich, almost legendary histories and prefer badges that reflect their heritage, and, mean more than a stock catalog badge. The Texas Rangers, the U.S. Marshals, are only two examples. The 26-man Arizona Rangers, in existence initially from 1901 to 1909, wore large solid sheet silver five-point stars, hand-engraved.
  The Dallas Police use a unique, large 5-point star, surrounded by banners, with a large "D" center (for 'big-D'). After President Kennedy was assassinated in 1963, the "D" in the badges was shaded black and worn that way until 1972, when they were silver or gold-colored once again.
Zdes' rasskazana istoriia piatikonechnyh zvezd v Tehase i Dallase.