---------------------------------------------------------------
Syn Len 2-Unit Edge | 1 Syn Vol| sqrt(72) Syn Vol |
| 1/3 Cart Vol| sqrt(8) Cart Vol |
---------------------------------------------------------------
xyz Len Unit Edge | 1/sqrt(8) Syn Vol| 3 Syn Vol |
| 1/sqrt(72) Cart Vol| 1 Cart Vol |
All else being equal the following conversions apply
tet -> cube - 1/sqrt(72)
Syn Vol->Cart Vol - 1/3
Syn Len->Cart Len - 1/sqrt(2)
Syn Len Conventional Calc'd Vol->Cart Vol - 1/sqrt(8)
Combining the the fourth and second conversions
Syn Len Conventional Calc'd Vol->Syn Vol - sqrt(9/8)
Column 1, Row 1:
In the Synergetics system a tetrahedron with edge length 2
has a volume of 1. Viewing this same tetrahedron from
within the XYZ system its volume is 1/3
Column 1 Row 2:
In the XYZ system a tetrahedron with edge length 1
has a volume of 1/sqrt(72). Viewing this same tetrahedron
from within the Synergetics system its volume is 1/sqrt(8)
Column 2, Row 1:
In the Synergetics system a cube with edge length 2
has a volume of sqrt(72). Viewing this same cube from
within the XYZ system its volume is sqrt(8)
Column 2 Row 2:
In the XYZ system a cube with edge length 1
has a volume of 1. Viewing this same cube from
within the Synergetics system its volume is 3.
vrml of 3 cube graphic
from the smallest to the largest cube
synergetic tet edge = sqrt(2) xyz tet edge = 1
synergetic cube edge = 1 xyz cube edge = .707
synergetic tet edge = 2 xyz tet edge = sqrt(2)
synergetic cube edge = sqrt(2) xyz cube edge = 1
synergetic tet edge = 2.8284 xyz tet edge = 2
synergetic cube edge = 2 xyz cube edge = sqrt(2)
