## Sunday, November 17, 2019

### A STEM Project: A Bethlehem Star Model and Instructions On How To Construct A Pyramid Using The Silhouette Software

The Bethlehem Star

The Bethlehem Star is the same construction as the Moravian star.  It is a 26 point star. The difference is that the Bethlehem star has pyramids of varying size. I have done all the work for you on constructing the pyramids.  I have added at the end of this post instructions on how to construct pyramids using the Silhouette software if you would like to learn how to make pyramids.

This Bethlehem Star is a 26 point star. It has 1 extra large pyramid, 1 large pyramid, 12 medium pyramids, and 4 small pyramids.  It also has 8 triangular pyramids. It is built on a base which is a rhombicuboctahedron. A rhombicuboctahedron is an Archimedean solid with eight triangular faces and eighteen square faces.

Here is the PDF file.  I used 65 lb. cardstock.

Here is the .Studio file.

Layout all of the pieces to make the Bethlehem Star

Fold the three strips of paper

Glue them into an octagon.

Apply glue on the two opposite squares of one octagonal strip.  Slip the other octagonal strip over the glued area to form a structure as shown in the photo above.

Apply glue on the four middle squares as shown above.

Slide the third octagonal strip over the glued areas. This structure is now called a small rhombicuboctahedron

Fold the perforations of the triangular pyramid. Apply glue on the left side which looks like a triangle.

Completed triangular pyramid.  Repeat for the remaining seven triangular pyramids. Set these aside.  These pyramids will be the last to be glued to the model.

Bend the four sided pyramid and apply glue as shown.

Four sided pyramid.

If you want to hang up your Bethlehem star, tape a string in the center of the large pyramid. The large pyramid is the second largest pyramid size.

Glue the large pyramid closed and allow the string to protrude from the center apex of the pyramid. Glue all the remaining pyramids together and sort them according to size.

The large pyramid is glued to the top. and the extra large pyramid is glued to the bottom.

The four small pyramids are glued in the middle squares as shown above.

Notice the placement of the triangles and squares.  The squares are where the four sided medium pyramids are glued.  At this time, you have twelve medium sized pyramids.  They will be glued to each of the squares.

Using the medium pyramid, bend two of the tabs inward and the opposite tabs outward. Apply glue to the tabs as shown above.

The two flaps will be bent under the small rhombicuboctahedron. Notice in the above photo, the tabs are attached inside the small rhombicuboctahedron. Repeat until all of the medium sized pyramids are attached.

The last thing to do is to glue in the triangular pyramids. Apply glue to the triangular pyramid and insert into the triangle.  Repeat for the remaining triangular pyramids.

Completed Bethlehem Star - Notice how big it is based on my ruler. It's huge!

Instructions on how to make pyramids using the Silhouette software:

In making this Bethlehem Star, I had to make each pyramid separately as the pyramid can not be resized to have the same base length.  The base length in this case is one inch.  I had to make a pyramid with a base of one inch and then a height that I perceived would look good on the star.

Here is how to make a pyramid using the Silhouette software. Using the Draw Polygon symbol shown in the top left corner of the picture above.  (Turn on your grid so that you see that the triangle is drawn correctly.)

Make a triangle that has a base of one inch. You can do so by using the Transform Scale window and changing the width to one inch.

In Pointing editing mode, break the path of all of the three points.  The points will turn from black to red when they are broken. In the Object menu, release the compound path. Change one of the sides to a dotted line, as shown above.

Measure the angle of the triangle by using the flexishape arc tool. the arc tool is the first shape.

Trace over the three points of the triangle using the flexishape tool.  I moved the flexishape so that you can see what was created.  At the top of the flexishape, the measurement of the top angle is 32 degrees.  This measurement is needed to rotate the triangle to form the pyramid.  You can delete the flexishape as this is no longer needed.

In the advanced replicate window, I rotated the shape 32 degrees.  Keep rotating the shape as many times as you need to create your pyramid.

Here is the figure with the excess interior lines removed.

Duplicate the right hand dotted line.

Change the dotted line to a solid line.  In point editing mode, create a point and attach this solid line to the figure. Your pyramid is now complete.  You can use these same instructions for a pyramid with as many sides that you want.