6-Armed and Higher-Armed Magic Ghost Number Star Polyhedra In A 3-Dimensional Space

I am not quite reaching a perfect match with the Outer Ghost Numbers derived from the Inner Ghost Number spatial-diagonals, resulting from different face combinations on higher star polyhedron other than a 6-armed star polyhedron.

On a 6-armed star polyhedron, the calculations work out perfectly. This, I believe, is because a 6-armed star polyhedron is equal to a Magic Ghost Number Cube in that it holds the maximum 8 vertices or corners around a central position, producing the maximum octrants that can exist in our 3-D space.

If you are not familiar with my term Octrant, it is simply an extension of the 4 flat quadrants of the Cartesian coordinate plane extended into space: Octrants! The 8 maximum zones of a 3-D spatial coordinate system. There might be an already established name, but I'll stick with Octrant.

The Central and Outer Ghost Numbers of a 6-armed star polyhedron, numbered 1 to 24 is 300.

I calculated the Central Ghost Number of these higher polyhedra, numbered 1 to 60 and it comes out to 1,830. But I can't find any Outer Ghost Numbers to prove it in the usual spatial-diagonal way.

The same thing happens with higher regular polyhedra, there is a mismatch due to the more than 8 vertices that fill out 3D space with 8 maximum octrants. There is something really mysterious about how higher polyhedra fits into a 3D space, as far as the ghost numbers are concerned and I will work on understanding this more.

This is a link to all my Magic Ghost Number research so far:
   • Latest Advances in My Magic Ghost Num...  

#linearalgebra #matrices #matrix #diagonal #commutativeproperty #commutative #innerproductspace #star #polyhedron #polyhedra #3d #threedimensional #space #spatial #spacetime