On Symmetric Structures within Symmetric Solid Objects

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

Top Of Page

Section XXVI - Defining Great-Circles , Great-Circle-Planes and Great-Circle-Arcs

Summary for the Section :

• In this Section , we shall define the 3 terms :
  • the [ Great-Circle Plane ] ,
  • the [ Great-Circle ] , and
  • the [ Great-Circle Arc ] ;

    for our use in the next 5 Sections and beyond , for the construction of the Spherical Solid Objects .

go to Top Of Page

The Definitions for the 3 terms :

• For our definitions , we first construct a Sphere of radius [ R ] and we identify the [ Center Point ] of the Sphere ,
  • as marked-off in [ blue-color ] in the diagram on-the-left below .

  

  We then have the following definitions :

  • A [ Great-Circle Plane ] is simply any [ plane ] that passes thru the [ Center Point ] of the Sphere .

  • A [ Great-Circle ] is the intersection of the [ Great-Circle Plane ] with the [ Sphere ] .

  • A [ Great-Circle Arc ] is then any sub-section / part of of a [ Great-Circle ] .

• And we shall be using exclusively [ Great-Circle Arcs ] to the divide the [ surface of the Sphere ] into sub-sections / pieces .

go to Top Of Page

go to the next section : Section XXVII - The Tetrahedral Sphere ( 4-Split )

go to the last section : Section XXV - [ Quad-Type Structures ] within the Icosahedron

return to the Symmetric Solid Objects HomePage

Original dated 2010-3-31