The general form of the cross, where the arms flare out from the center, is known as a cross pattée.  In this case the chestahedral cross is a “wedge” version of this.  There are many historical variants.  However, it seems that the chestahedral cross is most kin to two different versions of the cross pattée:  one is a version of the Cross of St. George, the other is the Maltese cross.

This cross, with the wide inner width and flat outer feet, is used in the Swedish Rite of Freemasonry in Sweden and Scandinavia.  It is a version of the St. George’s cross, which usually has non-triangular arms:

The other cross is the Maltese cross:

This cross requires noticing the three-dimensionality of the form.  The Maltese cross, with its eight points, is a symbol of an order of Christian warriors, the Knights of Malta, or the Knights Hospitaller, and has a “V” shape to the arms.  This group was originally founded around 1023 to provide care for poor, sick, or injured pilgrims to the Holy Land, and later became a religious and military order under its own charter, charged with the defense of the Holy Land.

So the chestahedral cross has two Maltese crosses and two crosses of St. George.  What was fascinating to discover is that these same forms show up also in the chestahedral star:

Who would have thought that all this would come from the chestahedron!  The many equilateral triangles on each form allow for many possible configurations…