(5) Design of sphere_Spherical rhombus triacontahedron

  I created a 30-sided dice like the one in the picture below, and based on this, I'm thinking of making a spherical design on top of the ball.



  This 30-sided die is a rhombus triacontahedron, one of the Catalan Solid with 30 rhombus faces. A Catalan Solid satisfies the following:

   i) Any edge connects exactly two vertices.

   ii) Any edge connects exactly two faces.

3D Printing Model


  We will discuss the details later in the section on polyhedra, but to sum up, the Catalan Solid are the dual polyhedra of the Archimedean Solid. This rhombic triacontahedron is the dual polyhedron of the icosidodecahedron.

 

  Now, let's implement a rhombus triacontahedron on a sphere. (Here, this spherical rhombus triacontahedron is one of the similar shapes of the rhombus triacontahedron.)

 

  First, mark all the vertices of the icosahedron and dodecahedron on the ball with [Spherical icodo].


  Each vertex of an icosahedron is connected to the vertices of the five adjacent dodecahedrons by arcs of great circles.


  If you connect the arcs of great circles in this way from the vertices of all other regular icosahedrons, you will complete the spherical rhombus triacontahedron.



  Let's try making a spherical design or spherical painting based on this spherical rhombus triacontahedron. Below is an example.


Ⓒ msolid

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