The 30-Rhombus Symmetric Solid Object HomePage
On the 30-Rhombus Symmetric Solid Object
by Frank C. Fung ( 1st published in February, 2013. )
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Summary and Key Findings :
The [ 30-Rhombus Symmetric Solid Object ] is characterized by :
the 30 rhombuses being identical to one-another in both shape and size , and
the centroids of the 30 rhombuses being equi-distant from the center of the said Symmetric Solid Object .
And the [ 30-Rhombus Symmetric Solid Object ] does exhibit Bi-Symmetric , Tri-Symmetric and Penta-Symmetric properties .
Table of Content
Table Of Content
Part I --- Introduction and Preliminaries
Section I
Introduction
Part II --- Constructing the [ 30-Rhombus Symmetric Solid Object ]
Section II
Outline on the Method of Construction
Section III
A Quick Review of the Pentagon
Section IV
Structural Dimensioning of the Dodecahedron
Section V
A Quick Review of the Equilateral Triangle
Section VI
Structural Dimensioning of the Icosahedron
Section VII
A Quick Review of the Rhombus
Section VIII
First Attempt at the [ 30-Rhombus Symmetric Solid Object ]
Section IX
Second Attempt at the [ 30-Rhombus Symmetric Solid Object ]
Section X
Third Attempt at the [ 30-Rhombus Symmetric Solid Object ]
Part III --- Properties of the[ 30-Rhombus Symmetric Solid Object ]
Section XI
[ Axis of Penta-Symmetry ] within the [ 30-Rhombus S-S-O ]
Section XII
[ Axis of Bi-Symmetry ] within the [ 30-Rhombus S-S-O ]
Section XIII
Five (5) [ Hexa-Symmetric Structures ] within the [ 30-Rhombus S-S-O ]
Section XIV
Six (6) sets of Parallel Edgess within the [ 30-Rhombus S-S-O ]
Section XV
[ Axis of Tri-Symmetry ] within the [ 30-Rhombus S-S-O ]
Section XVI
Co-Planar Axis within the [ 30-Rhombus S-S-O ]
Part IV --- Calculating the Tangent of 9 degrees
Section XVII
Reason for calculating the [ Tangent of 9-degrees ]
Section XVIII
Bringing-in the Tangent Addition Formula
Section XIX
Setting up the Equation for [ Tangent of 9-degrees ]
Section XX
Solving the Equation for the [ Tangent of 9-degrees ]
Part V --- The [ 12-Rhombus Symmetric Solid Object ]
Section XXI
Constructing the [ 12-Rhombus Symmetric Solid Object ]
Part VI --- Miscelleneous Related Issues
Section XXII
Investigating a different kind of Hexa-Symmetry
Part VII --- Concluding Remarks
Section XXIII
Concluding Remarks
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Original dated 2013-2-04