(4) Design of sphere_Designing a sphere using [Spherical icodo]

 Continuing from the previous episode, this time let's draw a design using the parish [Spherical icodo].

 

④ Using the parish [Spherical icodo], mark the 20 vertices of the regular dodecahedron on a white ball. Then, mark the midpoint (the red dot in the second picture below) between all the vertices.


Connect the midpoints with a [great circle ruler] so that a spherical pentagon is drawn on one face of the spherical dodecahedron.

This process is repeated on all faces of the spherical dodecahedron.

If you erase the line segments and vertices inside a spherical pentagon, it will look like the picture below.

By varying the coloring as shown below, you can complete many different designs.




⑤ Let's use the parish [Spherical icodo] to mark the 12 vertices of an icosahedron on the ball pool.

The midpoint is located between two adjacent vertices.

Connects a suitable curve from one vertex to the five adjacent midpoints.

If you draw this curve at every vertex, it is complete.



The above content is only a partial introduction to the book ‘design of sphere and Regular Polyhedrons’, so you can draw more diverse designs by referring to this book.

 

​​In the next part, we will cover solid geometry again. After introducing a few solid geometry, we will cover spherical painting, which is a more advanced form of spherical design.

 


Ⓒ msolid

Comments

Post a Comment

Popular posts from this blog

(9) Marking the vertices of a cuboctahedron on a sphere

Image
   Using [Spherical octacu], mark the vertices of a regular octahedron on the ball. (The photo below shows the arc of a great circle drawn.)   By taking the midpoints of the 12 great circles connecting the vertices of a regular octahedron and connecting these midpoints with arcs of the great circles, a cuboctahedron on the sphere is drawn.   From the beginning, mark only the vertices of the regular octahedron, and then use the scale of the great atom to mark only the midpoints of two adjacent vertices. These points are the vertices of the cuboctahedron on the sphere.     If you erase the regular octahedron, only the cuboctahedron remains.   The process of obtaining a cuboctahedron from a cube is also the same.   Ⓒ msolid  
Read more

(1) Design of sphere_Drawing a regular polyhedron on a sphere

Image
  How can we draw Platonic solids on a sphere? First, it is easy to mark the first point on the ball pit. However, it is not easy to find the location of the second point on the regular polyhedron. Furthermore, even if two points are marked, it is difficult to draw a straight line (in fact, a curve) on the sphere connecting these two points. However, if you use [Spherical octacu] and [Spherical icodo], and a [great circle ruler], you can easily draw a spherical regular polyhedron. [Spherical octacu] [Spherical icodo] [great circle ruler]   After inserting the ballpoint pen into [Spherical octacu] , mark all the marked holes with a name pen as shown in the enlarged photo below. These are the vertices of a regular octahedron. Mark all the unmarked holes with a name pen. These are the vertices of a regular cube. Likewise, if you put a ball in [Spherical icodo] and use a name pen to mark all the dots in the marked holes in the enlarged photo below, they are the vertices of a regu...
Read more

(2) Design of sphere_Tessellation of a sphere using a great circle

Image
  ① Tessellation of a cube   Using [Spherical octacu], mark the eight corners of a regular cube on a white ball. (You can also mark the corners of a regular octahedron.) Next, connect the dots on the ball to form an arc. Color the divided surfaces alternately. ② Tessellation of a regular octahedron   Using [Spherical octacu], mark the six vertices of a regular octahedron on a white ball, then mark the centers of the eight spherical triangles. (You can also mark the eight vertices of a regular cube using [Spherical octacu].) With 14 points marked, connect all neighboring points with an arc of a great circle. Just paint each divided side alternately orange. ③ Tessellation of the icosahedron   Using [Spherical icodo], mark the 12 vertices of an icosahedron on a white ball. Connect the 12 vertices with an arc of a circle. Now, let's connect the two vertices that are a bit further apart with an arc of the great circle. By painting each side alternately, you wi...
Read more