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.
https://drive.google.com/file/d/1sN1hp8WYtXhZQ6LHzFtFO_UEFSExPWLf/view?usp=sharing

Here is the .Studio file.
https://drive.google.com/file/d/1Nhicqqnc6AhuM4R0n3sr0ZXRMR3c0xBc/view?usp=sharing

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.  




Saturday, November 16, 2019

A STEM Project: A Moravian Star Model


A Moravian Star


I have always been fascinated by the look of the Moravian star. I love the way that the pyramids radiate from the center. I guess it appeals to my mathematical side.  In fact, the origin of this design originated as a geometry lesson in a Moravian Boys school in Niesky, Germany in the 1830's.  Students would make shapes out of paper and glue them together. The results were stellations or stars. This star was adopted by the Moravian Church as an advent symbol and is commonly used in nativity scenes to represent the star of Bethlehem. Traditionally, the star is hung the first Sunday of Advent and remains up until Epiphany, January 6, or the time of the coming of the Magi.

This Moravian star is a 26 point star. It has 18 large points and 8 small points. 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.
https://drive.google.com/file/d/1JolhWICmJxlC7aen1-CqpDvi4ZjM91Kr/view?usp=sharing

Here is the .Studio file.
https://drive.google.com/file/d/1ihzLN7tdll_koeN4tXdOisMcRKyJxAFp/view?usp=sharing

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 small isoceles triangular pyramid. Apply glue on the left side which looks like a triangle. 

Completed small isosceles triangular pyramid.  Repeat for the remaining isosceles triangular pyramids.

Bend the large isosceles pyramid and apply glue as shown.

Large isosceles pyramid. 

Glue all of the large isooceles pyramids.  If you want to hang up your Moravian star, tape a string in the center of the large isosceles pyramid.

Glue the large isosceles pyramid closed and allow the string to protrude from the center apex of the pyramid.

Completed parts before final assembly.

Glue the large isosceles pyramid to the top as shown with the tabs attached to the adjacent squares. Glue another isosceles pyramid to the bottom.

Repeat gluing the large isosceles pyramids to the four cardinal points as shown. 

Using the large isosceles 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.  In other words, every spot where there is a square next to an open triangle, you will use this method of attaching the large isosceles pyramid. Notice in the above photo, the tabs are attached inside the small rhombicuboctahedron.   Repeat until all of the large isosceles pyramids are attached.

Here is a photo of all the large isosceles pyramids attached. The only thing left to do is attach the small isosceles triangular pyramids.

Apply glue to the isosceles triangular pyramid tabs and insert it into the open equalateral triangle. Repeat for the other isosceles triangular pyramids.

Completed Moravian Star



After completing the Moravian Star, you might like to try my next model, the Bethlehem Star. https://papercraftetc.blogspot.com/2019/11/a-stem-project-bethlehem-star-model-and.html  It uses the same construction as the Moravian Star but the pyramid sizes vary.

A STEM Project: A Great Stellated Dodecahedron Model

A Great Stellated Dodecahedron 

A convex regular icosahedron is the foundation for making this great stellated dodecahedron.  Stellated means "star-like".  The icosahedron is transformed into a star-like polyhedron by attaching twenty isosceles triangular pyramids. A great stellated dodecahedron has 12 faces, 20 vertices and 30 edges.  


The convex regular dodecahedron is one of the five regular Platonic solidsThe convex regular dodecahedron has three stellations, all of which are regular star dodecahedra. They are the small stellated dodecahedron, the great dodecahedron. and great stellated dodecahedron. I made the small stellated dodecahedron in a previous post. https://papercraftetc.blogspot.com/2019/11/a-stem-project-small-stellated.html  and the great dodecahedron in a previous post. https://papercraftetc.blogspot.com/2019/11/a-stem-project-great-dodecahedron.html Here I will be making the great stellated dodecahedron.


This video depicts the transformation from a dodecahedron to other stellations. 



Please note, this model requires patience in gluing.  It is not hard to put it together but drying time is crucial. I used Aleene's Fast Grab Tacky glue.

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

https://drive.google.com/file/d/1k0VTfySR5dNanOk-cy-hNM0ZKsaD9xiG/view?usp=sharing


Here is the .Studio file.
https://drive.google.com/file/d/1FvSnAitr9ps7AeEvnrPwTsOML01kaCsl/view?usp=sharing


Fold the perforations on the icosahedron.

Glue the tabs to form the icosahedron.

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

Adhere into a pyramid shape.  Repeat to make 18 more isosceles triangular pyramids.

I folded the tabs of the base as shown so that they would lay flat for gluing.

Glue the isosceles triangular pyramid to the icosahedron. In this photo, I am showing the amount of glue that I applied to the icosahedron and a picture of the glue that I used.

Tape a string in the middle of the last triangular pyramid.  This will allow you to hang up the model. Apply glue on the triangle tab and make sure that the string protrudes from the top at the apex of the pyramid.

Completed Great Stellated Dodecahedron