$ icosa crystal structure NOT "tied to a definition" of the meter; But, rather "accountability" to a meter. The TYPiCAL crystallographical topology CAN'T uniformly describe crystal groups in terms of a STANDARD volume and edge. Unity isn't restricted to edge-lengths. NOTE: iSOTOPiC FiNE STRUCTURE Mass & SHAPEfactor 666.!! "COMMON & GENERAL structure" has to do with (about) Euclidean "SHAPE". And so, therefore, STRUCTURE PRE-defines ALL of the iNTEGER NUMBERs. [Sqrt5 = diagonal of double squares; Sqrt2 = diagonal of square.] A "VOLUME to SURFACE area" quotient can QUANTiFY a particular "SHAPE" (but a shape QUANTiTY WiTHOUT having PARTiCULARly-known "STRUCTURE"): EXAMPLEs: Vol / surface = m^3 / m^2 = Amp / (->H) = diameter / 6. WHERE: 1. Diameter / 6 implies a Euclidean sphere. 2. Edgelength / 6 implies a cube. 3. Triakis-icosahedron tip to tip / 6 , an iCOSA CORE symmetry. What this means is that if either of these has a diameter, edgelength or tip to tip of six (6) units (of ANY Unit System}, that STRUCTURE has a very simple 'Volume to Surface Area' QUOTiENT = ONE (1) unit. [Made memorable SiMPLY as 6,6,6; (SPHERE, CUBE, TriAKiS-iCOSAHEDRON).] Note THESE are the ONLY three STRUCTUREs which CORRESPOND in THiS way. Go see: < a SPACE.wpd > attached to < info-itsy-bitsy bytes it >.!! #######editing.. /6 /6 /6 A sphere, cube, and golden rhombic triakisicosahedron share a common equation of volume to surface area ratio of diameter / 6, edgelength / 6, and tip-to-tip / 6, ..respectively, all = scaling factor / 6. The volume to surface area ratio of each will be unity if the sphere has a diameter of six units, the cube has an edgelength of six units, and the golden rhombic triakisicosahedron has a golden rhombic lattice long diagonal of six units, as well. This gives a sphere volume of 36*pi=113.0973 cubic units, a cube volume of exactly 216 cubic units, and a golden rhombic triakisicosahedron volume of exactly 667.4767 cubic units, each with a volume to surface area ratio of one ..unity. A golden rhombic triakisicosahedron is an icosahedral crystal core, with 20 golden parallelipiped unit-cells. This initial nucleus of twenty golden rhombohedral cells is a golden rhombic triakisicosahedron ..see the attached. Golden rhombic triakisicosahedra ..20-fold RADiAL symmetry. Golden rhombic parallelipiped unit-cells, with pointed-end angles of arctan 2 degrees, are the all-space-filling and can be stacked around the icosahedral cyrstal core-cluster of 20 unit-cells, maintaining the radial symmetry. An icosahedral crystal is a composite of 20 golden rhombic parallelipiped sectors. It has central angles of arctan 2 degrees, which is the central angles of a regular icosahedron & golden rhombic triakisicosahedron, --the apex angles of golden rhombii, triacontahedra and the Great Pyramid of Egypt. A triacontahedron is a six dimensional cube and twelve will exactly close-pack all space around a golden rhombic triakisicosahedron. It has 30 golden rhombus faces. The long to short diagonal ratio of a golden rhombus is phi --the golden ‘diamond' diagonal ratio, in this case. The area of one side of a golden rhombus is the short diagonal multiplied by the long diagonal, divided by 2. Go to: < http://www.georgehart.com/virtual-polyhedra/vp.html > Select: ‘Stellations of the Rhombic Triacontahedron' Choose: ‘list of models' See: #26 (U) (5 colors) --for the golden rhombic triakisicosahedron See: #1 core (5 colors) --for the golden rhombic triacontahedron --right click on the objects to select stick-view, and spin. Choose: ‘background' --to view stills of both the triacontahedron and triakisicosahedron on one page. Both of these are 5-cube composites in a circumsphere. The 30 golden rhombic faces of a triacontahedron are uniform portions of 30 faces of 5 composite cubes. The 20 tips of the golden rhombic triakisicosahedron mark the 40 corners of 5 composite cubes. Together, these two are all-space-filling. With triacontahedra as hubs and the triakisicosahedra as struts, these two also can form all of the golden rhombic isozonohedra. Yours truly, `````arcsign````` VERY sincerely u c, ```Brian