In this class we make a pentagon medal with an internal star at the center.
 To help the attendant to understand the folding diagram, a rectangular vellum
sheet is used in a practice folding exercise. Result shown in Fig 1-1.
The final target is to make a nice art piece as shown in Fig 1-2 using a paper 
with folding lines and five axis symmetric pattern printed. 

The first step is to cut out a pentagon from a square or rectangular paper. 
Here a commercially available light weight vellum paper is used. 
The procedure is shown in the following web site.
 "How to Make a Decagon" 
URL:  http://origami.oschene.com/cp/DEcagon%20SCP.pdf by Philip Chapman-Bell .

The reason I like this method is that most of  the lines created in the process 
is used effectively when this model is folded.
At the end of the original PDF file, a small drawing is added to show
the discrepancy of this method against the exact pentagon geometry.

For clarity purposes, the front side of the paper is shown in white, and back side in black. 
The whole process is described  in 16 steps on 2 pages  as shown in Fig 1-4A & Fig 1-4B.
In the drawing "red" color denotes "mountain (Yama) fold", and "blue", "valley (Tani)".

First fix the printed paper atop a heavy weight paper using tape.
Then score all the red and blue lines using a ruler and a ball point pen.
After scoring is done, peel off the scored paper.
Using a scissor, cut along the outer pentagon boundary lines.
Precrease mountain fold lines, then valley fold lines.
Construction is similar to the process used in the vellum exercise session.

If you observe the two pictures above (Fig 1-5A & 5B), it is clear
that Fig 1-5A is a composite of one symmetric image and Fig 1-5B.
This suggests that anyone can create his own folding diagram 
if Fig 1-5B is printed over any image available.

In this class we make a pentagon medal with an opening at the center.
 To help the attendant to understand the folding diagram, a rectangular vellum
sheet is used in a practice folding exercise. Result shown in Fig 2-1.
The final target is to make a nice art piece as shown in Fig 2-2 using a paper 
with folding lines and five axis symmetric pattern printed. 

The first step is to cut out a pentagon from a square or rectangular paper. 
Here a commercially available light weight vellum paper is used. 
The procedure is shown in the following web site.
 "How to Make a Decagon" 
URL:  http://origami.oschene.com/cp/DEcagon%20SCP.pdf by Philip Chapman-Bell .

The reason I like this method is that most of  the lines created in the process 
is used effectively when this model is folded.
At the end of the original PDF file, a small drawing is added to show
the discrepancy of this method against the exact pentagon geometry.

For clarity purposes, the front side of the paper is shown in white, and back side in gray. 
The whole process is described  in 16 steps on 2 pages  as shown in Fig 2-4A & Fig 2-4B.
In the drawing "red" color denotes "mountain (Yama) fold", and "blue", "valley (Tani)".

The paper prepared for this model has both front and back printed.  
The pattern on one side (Fig 2-5A) is a spiral pattern with multiple concentric
circles and this is the outside pattern in the finished model.
The other side (Fig 2-5B) has folding lines and the colored sections ,which
is the interior pattern of the model.
First fix the printed paper atop a heavy weight paper using tape.
Then score all the red and blue lines using a ruler and a ball point pen.
After scoring is done, peel off the scored paper.
Using a scissor, cut along the outer pentagon boundary lines.
Precrease mountain fold lines, then valley fold lines.
Construction is similar to the process used in the vellum exercise session.

It is very important that the centers of the two images above must be 
located very close. If not, the symmetry of the folded model is lost 
and the overall looks is not satisfactory to the eyes.

Here we will discuss how to apply some variations to these base model
and obtain the aesthetically satisfying models .
A few examples are shown in Fig 3-3A & 3B.
Fig 3-3A:  note that radii of the star in front and pentagon in the back are the same length.
Fig 3-3B:  note two overlapping pentagons at the center area.

Here we will discuss how to apply some variations to these base model
and obtain the aesthetically satisfying models .
A few examples are shown in Fig 3-3A & 3B.
Fig 3-3A:  note that radii of the star in front and pentagon in the back are the same length.
Fig 3-3B:  note two overlapping pentagons at the center area.

  

Observing these 2 figures,we notice that

1. In Type -I, somewhere between "C" and "D" ,the radii of the base pentagon and five-pointed-star
    become identical.

2. In Type - II, between "F" and "G", the red colored tip  will be partially hidden under the center pentagon.


How can we find the exact location ?

 The diagrams for case "B" and "D" are drawn on the same drawing.

     In the drawing,                            "B"        "D"

	      radius of the Star  :            0.702      2.351
 
              radius of the base pentagon  :   2.038      1.019

  This set of data are plotted as a graph , Star Radius ( red ) and Base Radius ( blue ).

 Two lines intersects at radius = 1.527, this is the radius of the diagram to be used.

 A new diagram is created and this is pasted over the separately prepared image file.

 Both are shown in the figures below.

 The diagrams for case "F" and "G" are drawn on the same drawing.

     In the drawing,                               "F"        "G"

	     length of "X"   :                   2.2546      2.2301 

              length of "Y"  :                   1.6832      1.2074

	     diameter of the base pentagon       1.0938      0.7846

              ( X - D)                           1.1608      1.4455

              ( X - D) - Y                      -0.5224      0.2381

  This set of data are plotted in a graph , parameters shown in different colors.

 Note the values of ( X - D) - Y.  They are the distance of overlapping we are looking for. 

 The point where RED colored line intersects with ordinate value = 0 is the point 

where the tip of the star touches the base pentagon. 

 For the actual choice of base pentagon dimension, this point is moved slightly

to the left to be safe.  Its value is 0.958. The diagram using this diameter is shown below.

  The final diagram for Model-II is created by inserting this diagram on the separately

prepared five axis symmetric image drawing.

 For this exercise another pattern is printed on the back side. Notice that the pattern 

on the back side is the mirror image of the same pattern with respect to the horizontal axis

through the center.