Magen David- Star of David
The Secret of the Star of David according to the Book Sod ha vi Leiriav Shaar aleph ot Koach:

The Star of David is made of 2 Triangles whose connection with each other creates a hexagram from which wings extend. That way the middle becomes stronger. When the outstanding wings are folded they cover exactly the body. The perfect cover of the 6 wings over the Body hints at the holy resin about which is said: Six wings six wings for one, two cover his face and two cover his legs and two fly.

Basically the Magen David hints to the 7 Spheres and pleas of Kabbalah. The six wings hint to the 6 Qualitys of the Heart:Chessed, Gevurah,Tifereth,Netzach, Hod,Yesod. They are mechanisms in the Books of Kabbalah and End.

The inner Hexagram hints to the royal sphere: Kabbalah calls this mechanism Heichal Hakadosch Baemtzah.

An outstanding example to this intention can be found in the Prayer of Birkat ha Haftarah. There the Magen David is mentioned.

2 Triangles-Segol and its biblical cantillation symbol:
In a deeper sense in an elevated root are all the spheres engaged in the Magen David (10 Spheres and 3 Heads that are in the Crown who are called the Crown of Priests, Crown of the Torah and the Crown of Kingdom)
And that links to 13 spiritual forces.

The 2 Triangles from which the Magen David is made stand against the sign of sagol in the Punctuation. And the Sign of biblical cantillation in different cantillation notes. It hints to the higher Triangle of the Spheres that belongs to the Area of Awareness-Keter,Chochma,Binah. Keter is in the middle, Chochmah is on the right and Binah is on the left side. Segol hints to the inferior triangle of the Spheres that belongs to the Area of Emotions-Chessed, Gevurah,Tifereth. The order is from right, Gevurah from left and Tifereth at the middle and from the bottom. Between the 2 Triangles of the Spheres stands the Sphere of Knowledge that designates and connects all. If so, when we draw all of those aspects we get that picture:
When we delve deep into that inner structure of 6 Points that show up on that picture the Points of the Segol on top and the Points of the Segol on the bottom of Worshipping of G'd will be pulled on the lines that connect between all these points.(from the Power of the Spheres of Knowledge that stands in the middle and connects between all the Aspects and Points).

3 Pillars of Worshipping G'd
Each triangle of the Spheres hints at the Lines in the Worshipping of G'd on which the world exists. "On three things stands/exists the world: On Torah, on Worshipping(Prayer,Worshipping of the Heart) of G'd, and on good deeds (Charity,including practical Mitzvot)".

In the superior Triangle (Keter,Chochma,Binah) Keter stands against the fulfillment of the Commandments, that are the desire of G'd(the desire is the external Power in the Keter-the bottom head between the 3 Heads on the Keter. And when we talk of the Keter in relation to the Spheres of Wisdom and Binah we talk of exteriority of the Keter only. The Keter Malchut is extern to the Keter and from there come the Commandments of the King. Chochmah is against the Study of Torah that is the Wisdom of G'd. And Binah is against the Prayer which is the observing inner worshipping.

In the inferior Triangle ( Chessed-Gevurah-Tiferet). Chessed is against Charity/good deeds (incl.all the Mitzvot), of course the Gevurah stands against the worshipping in Prayer in which man ascendes from his place towards above. Tifereth stands against the Study of Torah as known in Kabbalah (Tiferet is the outstanding quality of Yakov Avinu because he was sitting in the Tents -Tents of G'd, about him is said Give Truth to Yakov)

3 Types of Relations between G'd and Israel
In addition to the fact that each Triangle hints to the 3 Pillars of Worshipping G'd on which the world exists, each triangle also shows 3 types of how the relation is between the Jewish People and G'd. They are annotated in length in the Saying Awinu Malkeinu Dodeinu in the Book Ani le Dodi ve Dudi li)
1.Relation King-People
2.Relation Father-Son
3.Relation Man- Wife

In the superior Triangle the relations find their own expression in the 3 Pillars of Worshipping in this way: Desire of G'd expresses itself in the Sphere of the Keter- realized through cancellation of people to king and slave to his owner. Torah Study - the Wisdom of G'd the emerging and illuminating from the Spheres of the Wisdom- is happening like the Study of Son from Father. The Prayer( worshipping of Binah and the observance) is uniqueness and matching of Bride and Groom and the praying man and his G'd. On the content of the Binah is Simcha- Happiness and the Connection between Groom and Bride .

On the inferior Triangle the Relations are divided into the 3 Pillars of Worshipping in a different Way. Gemilut Chassadim is a son worshipping his father and therefore he follows his good ways."What is Gemilut Chassadim? (Awinu she Bashamayim) Also you are gomel Hassadim-and behave always kind and merciful in accordance to the law to please his father.( in contradiction to the past,the precise not to stray from the attribute of Law)

The Prayer - that belongs here to Gevurah and Din is the Worshipping to cross over to our Master. When he turns to him in Prayer "Ke Avda kamei meria"-Like Servant to our Master. Study of Torah-in the Sphere of Tiferet it is a Kiss between Groom and Bride since this is the place where the man's mouth learns and G'ds mouth unite in one speech-the speech of Torah matters, and this is how a kiss is created between them(Yichud ha Neshikin is special to the Sphere of Tiferet, the Quality of Yaakov Avinu, of whom is said ..and Yakov kissed Rachel)

The Painting of the Magen David
According to the Introductions you have to pull the lines between different points- the lines that can be pulled between every 2 points that belong to the same Pillar of Worshipping and the line to be pulled between every 2 points that express the same relation between G'd and Israel:
Pillar of Commandments- Pillar of Gemillut Chassadim- continued on the Keter of Chessed ,the Pillar of Torah continues from the Wisdom(Chochmah)to Tiferet and the Pillar of Tefila (Prayer) the Pillar of "Worship"-continues from Binah to Gevurah.And yes the relations King-People continue from the Keter to Gevurah,Father- son relations continue from Wisdom to Chessed and Husband- Wife relations continue from Binah to Tiferet. When we add to the Lines that can be pulled also the natural connections that are in each triangle. Like the connecting line between Keter and Chochma and Binah,and the connecting line between Chessed and Gevurah and Tiferet - we get a Magen David that is framed and checkerd inside the hexagram.

In the drawing are another 6 framed points- 6 Vertexes in the inner Hexagram,from where the Wings of the Magen David come out.:
Those 6 Points stand against the Heads and Spheres that are aleady mentioned (the explanation of these points is deep, and whoever is interested to widen his knowledge here should read the Book Sod ha Vi Leireiav)
The Point between Keter(Keter Malhut) and Chochma is the illumination from the second head of the Keter. The mechanism Risha Dain and the Content of it is the Power of Enjyment of the Spirit that is in the Secret of the Keter Torah.
The Point between Keter and Binah is an illumination from the highest head of the Keter- the mechanism Risha dla jeda velo Atida and its quality is Power of Faith- that is in the Secret of Keter ha Kehuna. The Point between Binah and Gevurahis the root the Sphere of Gevurah - end is a line on the left side(the line of the Sphere Chochmah-Chessed-Netzach)
The Point between Chessed and Tiferet is the root to the Sphere of Yesod. The Point between Gevura and Tiferet is the Root to the Sphere of Malchut. According to this are all 13 aspects hinted of the upper Spheres and Heads in the Drawing of the Magen David.

All the aspects that are mentioned till here are external names of the Spheres-names that were given to them in the Kabbalah- and everyone of those Spheres has its own internal names that explain their Spiritual Powers. The internal names are annotated in the Chasidut and study the 10 Spheres of Worshipping of G'd ( see further in the Book Sod ha Vi Leireiav Shaar aleph otiot 1-21)and this structure are hints in the 13 closed areas in the picture that appeared us from this connection.

12 closed areas around the inner hexagram are against 12 months of the year, when the additional 13th month in the intercalated year is the central area. And further 12 closed areas all around for the internal hexagram stand against 12 tribes that are assembled around the Tabernacle, and the central area stands against the Tribe of Levi that is camping close to the Tabernacle.

More on the Secret and on the impure Powers of the Magen David can be read in the Tikun Chawa that explains the integration of these 3 forms.