Islamic State in China

Ivan Sache published on the website of allstates-flag.com that the war lord Cheng-Chi-Tsai established an autonomous province in Xin-Jiang (1933-1942) and designed a yellow flag with a red six-pointed star. He later changed his flag to  a red field with a yellow six-pointed star.

Find The Differences

Hexagram Picture from Hisham's palace is courtesy of "markuscuel" who published it on Flickr. Picture of IDF emblem is copied from Wikipedia.
I changed the angle of the hexagram from Hisham's palace in photoshop in order to enable more convenient comparison between the two shapes.

IMHO Muslims who dislike the Star of David may look at it as an ancient Omayyad emblem. The hexagram is an inter-religious symbol. In the course of time it served Muslims, Christians, Jews and Budhists and there's no need to hate it just because it is identified currently with Israel and the Jews.

Jericho

This is a Muslim Six pointed Star from the eighth century C.E. in Hisham palace (Khirbet El-Mafjar) located 3 km north of Jericho. 

Picture is courtesy of "markuscuel" who published it on Flickr. 

This is not the only hexagram in Hisham's Palace:

a. K.A.C Creswell shows in his book (Early Muslim Architecture, Vo. I part 2, Oxford, 1969 p. 558) a window-grille reconstructed from fragments which had been printed red or brownish-gold, drawn on equilateral triangles network. There are several hexagrams and a six petaled rose in each of them.
b. In p.572 there's another photo of a grill from diwan of bath dated to 739-43 C.E.

Most Complexly Emotive of All Jewish Symbols

In The Age Website Chris Evans wrote on May 4, 2004 an article about a controversial artwork on display in Flinders Street in Melbourne, Victoria, Australia. The work shows a large Star of David painted on a wall along with Red text including statistic data concerning Israel's behavior towards the Palestenians.  

David Bernstein wrote on May 6 on the same Website: 

…the use of the Star of David in an indisputably hostile context was deliberately provocative. The Star of David is the most complexly emotive of all Jewish symbols: it has profound, ages-old religious significance as the most ubiquitous and recognisable of such symbols.

Dutch Navy

Mark Sensen wrote on Flags Of The World website about Command and Rank flags in The Dutch Navy since 1815

A Lieutenant-Admiral has four white sixpointed stars in the red stripe near the hoist of the tricolour…
A Vice-Admiral has three …A Rear-Admiral has two (side by side) …A Commodore has one.

He doesn’t explain why the Dutch Navy chose this shape and not any other shape.

Seal from Sidon

My Traffic Meter told me that my blog address appeared today on a Christian Forum. So I clicked the link and saw that "diamondjoust", who is a Junior Member in this Forum, asked:

Why do Jews use the symbol of a hexagram or Magen David?

and "baraqemet", who is a regular member in this Forum, mentioned in his answer the seal from the seventh century B.C.E. found in Sidon and belonging to one Joshua ben Asayahu which is mentioned in Gershom Sholem’s classical article about the Star of David. baraqemet commented:

All we have is a statement by someone [Gershom Sholem], who is into kabbalah, who did not supply any proof to support their theories. 

I don't want the bother of registering to the above-mentioned Forum but I happen to know the missing source:
David Diringer, Le Iscrizioni Antico-ebraiche Palestinesi, Pub; Icazioni Dell'Universita Di Firenze, Facolta' Di Lettere E Filosofia; 3, Firenze: Le Monnier, 1934, P. 187
Check it out!

Jali

Hexagram surrounded by six hexagons in a grid called Jali (indian term of "mashrabia").
Picture (taken at Humayun Tomb, India) is courtesy of "mattlogelin" who published it on Flickr.