03-18-2018, 03:56 PM

...

This is the difficult part,

trying to display the tetrahedral hexads,

attaching themselves:

to each and every Corner Angle of the Khafre Pyramid Octahedral.

I could not redraw the hexads,

to look like they are coming in at angles to the Corner Angles of the pyramid,

so this is the best I have to offer.

The upper half of the image shows:

the hexad coming in from the right hand side,

to the Corner Angle line.

It situates at a 90 degree angle,

to the hexad on the left hand side.

Each tetrahedral hexad,

as it positions itself on the pyramid Corner Angle slope lines,

P to D,

or P1 to D1 etc etc

sits at a 90 degree angle from each other tetrahedral hexad situated.

In the bottom half of the image,

the tetrahedral hexad <---

seen on the right hand side of the upper image <---

is now situated on the left,

so that the next hexad,

can be defined and situated on the next Corner Angle line

Note how each mound letter is designated with a number.

Note:

P, P1, P2, P3

are all the same points,

they are all essentially just point P

THE KEY -- to the -- Khafre Pyramid --SQUARE HEXADS {to be shown next post}

is in the upper image,

look at the lines:

P1 to DK --- then DK --down to P.

A 2D plane -- bisects the Octahedral -- through the P-DK lines <---

This is a key function to understand how the Square Hexad is situated.

The SQUARE HEXAD

is automatically formed,

when all the horizontal lines are drawn,

from:

G to G1 to G2 to G3 {and back to G}

A to A1 to A2 to A3 {and back to A}

and this same process for

B, D , and E <---

What happens when all these horizontal lines are drawn,

is that an exterior SOLID is formed,

that circumscribes the interior solid -- the Khafre Octahedral.

the main point:

when the 2D plane {along lines P -- to DK -- back down to P}

cross sects the entire Octahedral

{from both directions}

through the horizontal lines -- G to G1 to G2 to G3 {and back to G} etc etc

that form -- the exterior solid,

the Khafre Pyramid

SQUARE HEXAD

is automatically formed by the cross secting plane.

try and envision the exterior solid,

and the cross secting plane,

emerging through the horizontal lines:

G to G1 to G2 to G3 {and back to G}

A to A1 to A2 to A3 {and back to A}

and this same process for

B, D , and E <---

I will soon post the SQUARE HEXAD

automatically generated,

and the associated geometry therein.

...

This is the difficult part,

trying to display the tetrahedral hexads,

attaching themselves:

to each and every Corner Angle of the Khafre Pyramid Octahedral.

I could not redraw the hexads,

to look like they are coming in at angles to the Corner Angles of the pyramid,

so this is the best I have to offer.

The upper half of the image shows:

the hexad coming in from the right hand side,

to the Corner Angle line.

It situates at a 90 degree angle,

to the hexad on the left hand side.

Each tetrahedral hexad,

as it positions itself on the pyramid Corner Angle slope lines,

P to D,

or P1 to D1 etc etc

sits at a 90 degree angle from each other tetrahedral hexad situated.

In the bottom half of the image,

the tetrahedral hexad <---

seen on the right hand side of the upper image <---

is now situated on the left,

so that the next hexad,

can be defined and situated on the next Corner Angle line

Note how each mound letter is designated with a number.

Note:

P, P1, P2, P3

are all the same points,

they are all essentially just point P

THE KEY -- to the -- Khafre Pyramid --SQUARE HEXADS {to be shown next post}

is in the upper image,

look at the lines:

P1 to DK --- then DK --down to P.

A 2D plane -- bisects the Octahedral -- through the P-DK lines <---

This is a key function to understand how the Square Hexad is situated.

The SQUARE HEXAD

is automatically formed,

when all the horizontal lines are drawn,

from:

G to G1 to G2 to G3 {and back to G}

A to A1 to A2 to A3 {and back to A}

and this same process for

B, D , and E <---

What happens when all these horizontal lines are drawn,

is that an exterior SOLID is formed,

that circumscribes the interior solid -- the Khafre Octahedral.

the main point:

when the 2D plane {along lines P -- to DK -- back down to P}

cross sects the entire Octahedral

{from both directions}

through the horizontal lines -- G to G1 to G2 to G3 {and back to G} etc etc

that form -- the exterior solid,

the Khafre Pyramid

SQUARE HEXAD

is automatically formed by the cross secting plane.

try and envision the exterior solid,

and the cross secting plane,

emerging through the horizontal lines:

G to G1 to G2 to G3 {and back to G}

A to A1 to A2 to A3 {and back to A}

and this same process for

B, D , and E <---

I will soon post the SQUARE HEXAD

automatically generated,

and the associated geometry therein.

...