On Symmetric Structures within Symmetric Solid Objects

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

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Section VI - Basic Properties of the Dodecahedron

Summary for the Section :

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

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The Structure of the Dodecahedron :

• The Dodecahedron is simply a twelve-faced Symmetric Solid Object :
  • with each of the twelve (12) identical Faces being a Pentagon .

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

  

  • And we simply take note here that the Dodecahedron has exactly twenty (20) Nodal Points / Vertices .

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

  

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Taking note of the 60 Triangles :

• We also take note , at this point , of a set of 60 Triangles hidden inside the Dodecahedron , comprising of :
  • a set of 20 Triangles of equal-but-smaller-size , as marked-off in [ blue-color ] , and
  • a set of 40 Triangles of equal-but-bigger-size , as marked-off in [ green / magenta / cyan / yellow colors ] ,

    in the next 30 diagrams to follow .

  
  
  
  
  
  
  
  
  
  

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Intrinsic Shapes associated with the Dodecahedron :

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

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go to the next section : Section VII - Basic Properties of the Icosahedron

go to the last section : Section V - Basic Properties of the Octahedron

return to the Symmetric Solid Objects HomePage

Original dated 2010-3-31