Construction of an Alternate Cube of Space:
The Octahedron of Space
The Cube of Space diagram is based upon the Sepher Yetzirah, The Book of Formation. This oldest of Qabalistic texts contains no diagrams. It is usually assumed that the correspondences given there between the 22 Hebrew letters and the directions refer to a cube. However, they can equally be placed upon an octahedron. Here the placement of the 22 letters is shown with their corresponding Tarot keys. The positions on the cube are from the Sepher Yetzirah, short version (with one change by Paul Foster Case - the positions of lamed (Justice) and nun (Death) are reversed).

Note that the Hebrew alphabet contains seven "double" letters (each has two pronunciations), twelve "single" letters, and three "mother" letters. The cube has six faces plus the center = seven, twelve edges, and three axi through the center of the faces. Similarly, the octahedron has six vertexes (plus the center), twelve edges, and three axi. Indeed, in their geometry, both the cube and the octahedron are ideally suited to representing the three sets (3 mothers, 7 doubles, 12 singles) of Hebrew letters.

Diagram
Description
A solid cube.
The same cube, transparent with the hidden lines visible.
The three planetary directions: Above (The Magician), West (The Wheel of Fortune) and South (The Sun).
The other three surfaces of the cube: Below (The High Priestess), East (The Empress) and North (The Tower).
At the center of the Cube of Space is Saturn (The World). The six faces and center of the cube are the seven inner planets corresponding to the seven Hebrew double letters.
The three axi through the faces of the cube are Neptune (the Hanged Man - East-West as shown here), Uranus (The Fool - above-below) and Pluto (Judgement - North-South). These are the three outer or "higher octave" planets corresponding to the three Hebrew "mother" letters.
Here a dot has been placed at the center of each face of the cube.
Connecting the dots creates an octahedron, shown here as a solid figure.
Here the octahedron is shown transparent.
Dots removed, here is the octahedron within the cube.
On the cube of space, the six sides (and center) are the seven inner planets. These same six are located at the six vertexes of the octahedron.
The twelve edges of the Cube of Space are the twelve zodiacal signs corresponding to the twelve Hebrew single letters.
This is easier to see. Note that the octahedron also has twelve edges. Here is depected the edge, East-above (the Lovers, the Hebrew single letter Zain) on both the Cube of Space and the octahedron.
Here the seven planets are arranged upon the octahedron to allow space for the twelve zodiacal signs.
Here the Tarot keys corresponding to the twelve zodiacal signs have been placed upon the edges of the octahedron.
The three "mothers", the higher octave planets complete the 22 Tarot key major arcana; the 22 letters of the Hebrew alphabet.
It's a little easier to see without the surrounding cube.
The "Octahedron of Space" with all the graphics; a bit bigger.
For a larger, animated view of this sequence, click here.