Uploaded February 2026 | Updated September 2026, 2 weeks ago
On a Magic Hybrid Number Cube, the Central Ghost Number disappears among the Primary Number walls of the inner cube, making room for the Central Real Number. On a Dual Level Commutative Magic Hybrid Number Cube, the Outer Ghost Numbers disappear as well among the Inner Ghost Number walls, making room for the Outer Commutative Magic Hybrid Number Cube!
I give examples of commutative and apparently non-commutative Magic Hybrid Number Cube pairs where both levels check out correctly for the interior and exterior cubes when using modified
bifurcated interior/exterior 3-step matrices for these newly discovered Dual Level Commutative Magic Hybrid Number Cubes.
Final remarks: On a Magic Hybrid Number Cube, trying to suppress a ghost number makes it reappear somewhere else. On a Dual Level Commutative Magic Hybrid Number Cube, trying to suppress the commutative property makes it double up!
Previous video:
youtu.be/vjN1qBQTqEU?si=tuMPb_0f__JXLdPX
youtube.com/playlist?list=PL9ArnWI_cuWvHFHh6NwxTNa-F9dSyMkxR&si=VfVB-YuQF4y5uiJk
#linearalgebra #matrices #commutativeproperty #MagicCube #transformation
On a Magic Hybrid Number Cube, the Central Ghost Number disappears among the Primary Number walls of the inner cube, making room for the Central Real Number. On a Dual Level Commutative Magic Hybrid Number Cube, the Outer Ghost Numbers disappear as well among the Inner Ghost Number walls, making room for the Outer Commutative Magic Hybrid Number Cube!
I give examples of commutative and apparently non-commutative Magic Hybrid Number Cube pairs where both levels check out correctly for the interior and exterior cubes when using modified
bifurcated interior/exterior 3-step matrices for these newly discovered Dual Level Commutative Magic Hybrid Number Cubes.
Final remarks: On a Magic Hybrid Number Cube, trying to suppress a ghost number makes it reappear somewhere else. On a Dual Level Commutative Magic Hybrid Number Cube, trying to suppress the commutative property makes it double up!
Previous video:
youtu.be/vjN1qBQTqEU?si=tuMPb_0f__JXLdPX
youtube.com/playlist?list=PL9ArnWI_cuWvHFHh6NwxTNa-F9dSyMkxR&si=VfVB-YuQF4y5uiJk
#linearalgebra #matrices #commutativeproperty #MagicCube #transformation









![Magic Nested Dodecahedron And Icosahedron Outer Ghost Numbers And Secondary Number Equations
With a Magic Ghost Number Cube, determining its Outer Ghost Numbers are pretty straightforward and all eight Outer Ghost Numbers have a distinct position on all eight corners of the cube. And its Central Ghost Number divides the Outer Ghost Numbers by 3.
For any polyhedra higher than a cube, its Outer Ghost Number can only be determined thru a statistical average, built up by adding two opposing faces 5 pentagonal (in the case of a dodecahedron) and 3 triangular (in the case of an icosahedron) Inner Ghost Numbers apiece, together and then adding all those 6 sums (for the dodecahedron) and 10 sums (for the icosahedron) up and then that result divided by 6 (in the case of a dodecahedron) or 10 (in the case of an icosahedron) to get the average Outer Ghost Number, which will always be divisible by its Central Ghost Number by 5 (for the dodecahedron) and divisible by 3 (for the icosahedron).
There are no distinct positions of the Outer Ghost Numbers on the dodecahedron or icosahedron. Instead, it is one single Outer Ghost Number statistically spread around each objects outer surface.
Secondary Number Equations
As with a cube, higher polyhedra has their own Secondary Number Equations, that Im currently trying to discern.
[Theres one spoken error in this video. I say 9 bounces off of 7 to become 18. Its actually 16.]
https://youtube.com/playlist?list=PL9ArnWI_cuWvHFHh6NwxTNa-F9dSyMkxR&si=vYaTqFsSOL8dC24q
#polyhedra #cube #dodecahedron #icosohedron #magic Magic Nested Dodecahedron And Icosahedron Outer Ghost Numbers And Secondary Number Equations](https://i.ytimg.com/vi/c-GC7thEexs/mqdefault.jpg)
