SSO - Quasi-Cubic Sphere ( 6-Split )

On Symmetric Structures within Symmetric Solid Objects

Section XXVIII - The Quasi-Cubic Sphere ( 6-Split )

In this Section , we shall introduce the Quasi-Cubic Sphere :
- a sphere with its outer-surface divided into 6 [ equal parts ] .

Let us recall that the Cube is six-faced Symmetric Solid Object with exactly eight (8) [ nodal-points ] , and :
- the 8 [ nodal-points ] are all equi-distant from the [ centroid ] of Symmetric Solid Object .
This then permits us to put the 8 [ nodal-points ] onto the surface of a Sphere , so that :
- the 8 [ nodal-points ] are now all equi-distant from the [ center ] of the Sphere .
Let us now join the eight (8) [ nodal-points ] via [ Great-Circle Arcs ] and we have this Spherical Solid Object below :
- and this then is our { Quasi-Cubic Sphere } with a [ 6-Split ] .
Let us now take a quick look at the positions of the 6 { individual pieces } ,
- for a slightly better feel of the Spherical Solid Object .

We simply note here that the [ surface area ] of the Sphere is given by :
- [ Surface Area ] = 4 * [ pi ] * [ R-Square ]
The [ surface area ] of an [ Individual Piece ] here is then :
- { 4 * [ pi ] * [ R-Square ] } divided by [ 6 ] ,
or simply :
- [ pi ] * [ R-Square ] * [ 2 / 3 ] .