enneacontahedron within rhombic triacontahedron
from David B Koski
to kirby urner
dates Mar 15, 16, 2010
subject enneacontahedron within rh triac
Below is an enneacontahedron showing a red outlined face of a rhombic
triacontahedron that would circumscribe it. Note that the thin yellow
rhombus is coplanar with the red outlined rh triac face.
There is a smaller rhombic triacontahedron face that is fully shaded.
This would be the face of a two sizes smaller scaled down rhombic triacontahedron.
The image below illustrates the volume differential between the enneacontahedron
and the circumscribed rhombic triacontahedron. in the that two sizes scaled
down rhombic triacontahedra + the enneacontahedron = the overall rhombic
This is the folding process to get two rhombic triacontahedrons from
the volume differential between the rh triac and the enneacontahedron
[Fig 1: top view, bottom view ]
The initial fold cuts the green length so both halves of the green length
meet up. Since the green length is problematic with the five fold T-module
arrangements, it is conveniently rendered moot.
The yellow lengths describing the thin rhombus mate up with the one
on the underbelly 2 into one on both sides.
[Fig 2: top view, bottom view ]
Instead of adding more to this email I'll just send it, each chunk represents
a cluster of 4 T-modules or 1/30th of a rh triac.
The main point is the dissolution of the green length with its sqrt2
factor. Once that has been negated the rest is just rearranging lesser
scaled T-modules until the desired product is achieved.