Mormons

Mormons believe they belong to the Jewish lost tribe Ephraim, and that's why Judaism is so important for them. No wonder they use the Star of David:
The Salt Lake Assembly Hall is Victorian gothic building and a Star of David within a circle is placed high above each entrance. (Photo courtesy of Wikipedia).
Some of the Mormons believe that the Star of David got its shape from the Urim and Thummim that the Jewish High Priest carried on his chest.
Vincent Chapman published on 28 January 2005 a flag for the Mormon Church which contains a big Star of David in the center surrounded by twelve stars that stand for the twelve tribes and the twelve apostles. The former Mormon flag which was made in the 1800's by Emma Smith had a large 5 point star in the middle.
Utah Republican Mormon Senator, Orrin Hatch, is a Zionist and on his front door there's a Star of David.
Cecil McGavin in his book Mormonism and Masonry (2004) mentions that Joseph Smith, the founder of the Mormon Church, "was not a Jew yet he was pleased to display above the door in his historic Mansion House in Nauvoo, Illinois, a small gilt-covered six pointed star".

Little-Known Chapter

Mildenstein medal, with a Swastika on one side and a Star of David on the other 
Photograph courtesy of Arnon Goldfinger (c) 2014

Mark Weber, Director of the Institute for Historical Review, published an article about Zionism and the Third Reich and in it told the story of SS officer Leopold von Mildenstein and Zionist Federation official Kurt Tuchler who traveled to Palestine together and stayed there for six months in order to assess Zionist development. In 1934 von Mildenstein published twelve illustrated articles in Der Angriff. Der Angriff issued a special medal, with a Swastika on one side and a Star of David on the other, to commemorate the joint SS-Zionist visit.

In the introduction to this article Weber says that this is one of the stories belonging to the little-known wide-ranging collaboration between Zionism and Nazi authorities; I reckon it is a repressed chapter, certainly from the Zionist point of view.

P.S.
 See Arnon Goldfinger's 2012 documentary, The Flat, on:
https://www.youtube.com/watch?v=Z94u_5qLxXU#t=30

See Also:
en.wikipedia.org/wiki/The_Flat_(2011_film)

Color and Meaning

Stars of David appear in almost any imaginable color:
The one on the center of the Israeli flag is BLUE like the stripes of the flag which represents the Jewish prayer shawl (Tallith).
The emblem of the Israeli Emergency Medical Service is a RED Magen David – Red like blood? Red like the Red Cross?
The emblem of the Israeli College of Para-veterinary studies is GREEN, like the green ecological movements, like nature in spring.
Alexander Mishory in his Hebrew book "shuru Habitu Ureu " wrote that the colors of the yellow patch were YELLOW AND BLACK because in the western Christian culture they stand for treason and heresy and it was used to describe Judas in Christian art.

Stone Workshop Ein Yael

Star of David stone at a Workshop in Ein Yael, Jerusalem.

Alchemy

Carl G Liungman wrote on his book Encyclopedia of Western Signs and Ideograms (2004, Page 256) that The Star of David serves as a general symbol of the art of alchemy and that it stands for a combination of water and fire. Sometimes it replaces the words "drink!" Or "swallow!" It is also a symbol for quintessence, the fifth element after air and earth and fire and water; which was believed to be the purest and essence of something.

On the New Alchemy Website I found a drawing from 1625 of Nature (Half naked Woman with four breasts, indicating wholeness) bearing the shinning Star of David - symbol of the lumen naturae (Light Of the Darkness, which illuminates it's own darkness, like exploring a dark cave with a candle, not with a torch).

Remo F. Roth wrote an online book titled The Archetype of the Holy Wedding in Alchemy and in the Unconscious of Modern Man where he says that the Star of David is used

In the mysticism of all five-world religions: in the Kabbalah, in Christian mysticism… in the heart chakra of Buddhist and Hindu Tantrism and in Muslim Sufism. It is always connected to the heart, the symbol of the Eros principle in the original and broadest sense of the word

Remo Roth's online book is an excellent introduction to Alchemy. I was taught there a lot of new and surprising things e.g. that the unity of the opposites, about which I heard a lot in Jewish sources, is in fact the main issue Alchemy deals with…

On the lamp - hexagram

Source: Musaeum Hermeticum  

alchemy book, Frankfurt, 1625

Source: Wikipedia Entry: Musaeum Hermeticum.

Ein Yael

Archaeologist Gershon Edelstein found a Christian Star of David in a mosaic floor in Ein Yael (En Yalu), in south Jerusalem’s Rephaim Valley, in a farm with a Roman villa from mid-third-century A.D. He wrote about it a long report from which I quote:
In the last week of the 1988 season, we uncovered the mosaic floor of the circular room of the bathhouse, a floor encircled by a triple-twisted rope pattern, familiar to us from the mosaics in the living area of the villa. However, to our surprise a double-twisted rope in the center forms a hexagram, the familiar six-pointed star, or Shield of David (in Hebrew, Magen David).
Yehudah Rapuano, who participated in the excavations, discusses in his article the possibility that this place commemorated Philip’s baptism of the eunuch, related in Acts 8.
I went to see this Star of David in the mosaic floor in Ein Yael and to take a photo of it, but it was taken for reconstruction and I don't know when they will put it back.

German Pentateuch

There's a Star of David on the c. 1300 illumination for the Duke of Sussex Pentateuch and in it there's an elephant. The book is located nowadays in the British Library in London.

On page 61 in his book Dreams of Subversion in Medieval Jewish Art and Literature (1997) Marc Michael Epstein claims that in the beginning of the 14th century for medieval German Jews the Star of David represented the Torah.

The Duke of Sussex's German Pentateuch was written and illuminated by a scribe-artist known as Hayyim, working in southern Germany around 1300