On Symmetric Structures within Symmetric Solid Objects

by Frank C. Fung ( 1st published in March, 2010. )

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Section VII - Basic Properties of the Icosahedron

Summary for the Section :

• In this Section , we shall take a quick look at the structure of the Icosahedron and some of its properties .

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The Structure of the Icosahedron :

• The Icosahedron is simply a twenty-faced Symmetric Solid Object :
  • with each of the twenty (20) identical Faces being a Triangle .

  We then present this set of 3 views for the Icosahedron :

  

  • And we simply take note here that the Icosahedron has exactly twelve (12) Nodal Points / Vertices .

• Let us now also bring in this set of 3 diagrams for a slightly better feel of the Icosahedron :
  • with the diagram in-the-middle being the Front View , and
  • with the diagram on-the-right being the Transparent View for the Back Pieces .

  

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Taking note of the 12 Pentagons :

• We also take note , at this point , of 12 Pentagons hidden inside the Icosahedron :

  
  
  
  

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Intrinsic Shapes associated with the Icosahedron :

• We simply take note here of the Icosahedron's primary involvement with Triangles and Pentagons .

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go to the next section : Section VIII - The Bi-Symmetric Nature of the Tetrahedron

go to the last section : Section VI - Basic Properties of the Dodecahedron

return to the Symmetric Solid Objects HomePage

Original dated 2010-3-31