The Leviathan Cross is sometimes referred to the cross of Satan, which means the "Satans Cross".
Depicted on the bottom is an infinity sign (∞),
and above is a double cross (‡). The Double cross symbolizes protection and balance between persons.
The infinity sign underlines the constant and infinite nature and most likely symbolizes the eternal universe, this may have
been used by Anton LaVey in The Satanic Bible to as a mockery of the cross,
to show that humans are their own centrum of balance, and truth.
This is what the ideology of Anton LaVey and the followers of the Church of Satan believe,
and this is what this symbol represents in this association.
An upside-down crucifix, however, is not a symbol of Satanism.
That would be referred to as "The Cross of St. Peter" since,
according to Origin of Alexandria, Simon Peter was crucified upside down.
In Alchemy, the Leviathan's cross is a symbol for sulfur,
which is one the three essential elements of nature.
In Asia, its name is the Brimstone Symbol.
The association with the Leviathan makes it a symbol of depth and surfacing.
The multiple crossroads of two crosses can be interpreted
as a sign of free choice, it can also be seen as a stroke-through
"equal-to" (=) to show that every person has their own life.
Sulfur (“Leviathan Cross”) A symbol for the alchemical element Sulfur, (Brimstone) which is spiritually analogous to the human soul.
Alchemically, sulfur has the qualities of masculine, hot and dry. Combined with Mercury (feminine, cool and moist), the pair were considered the parents of all metals.
Alchemical drawings often portray Sulfur as the sun. (In some views, sulfur and salt are the parents of Mercury) The symbol of sulfur is often used as an identifying symbol by Satanists, due to sulfur’s historical asociation with the devil.
This glyph is often referred to incorrectly as the “pontifical cross of Satan” by Christian tract writers, due to its adoption as an emblem of Satanism by Anton LaVey in the 1960s. The emblem has no history as a symbol of Satanism outside of LaVey’s usage, and the attribution is most likely a product of anti-Catholic sentiment, as it is often compared in this context to the Catholic Pontifical Cross. A more common symbol for sulfur is a fire triangle surmounting a cross of earth.
Origins
The Leviathan Cross was created by The Knights Templar. The symbol was then adopted by Anton LaVey, founder of the Church of Satan. Previous associations with the cross and Satanic foundations are unable to be identified.