Statement of Intent
In this project, the relationship between 2D and 3D shapes is explored and the transformation between the two is practiced through template making. Exercising the use of good craft and ideation, a 3D polyhedron will be made using a single sheet of Bristol paper (14”x 17” inch). The same polyhedron will be created again, but this time it is made with the modification option of negative space: cutting into the form creating negative shapes/ space inside the 3D polyhedron.
The materials used in this project are Bristol, glue, rulers, pencils, and a knife.
The final deliverables are comprised of a single pdf with photographs ( a minimum of 3 views), the templates/ net of, and instructions on how to build both polyhedrons.
Ideation
We first learned how to make a net for the cube.
I drew the layout of the net first knowing that a cube has a total of 6 sides.
I first drew 4 of the same dimension squares and stacked them vertically on top of one another. Then on the second square from the top, I added one square to each side creating a t-shaped net out of squares.
I knew that every 2 sides of the cube needs a tab to connect them, so I began to number/ color coded each side that would be put together. The hatch marks are the lines to score/ fold at.
Net of a Cube with Labeled Sides
Exercise 1A: Building the Perfect Cube
In this exercise, we were given the challenge to make the perfect.
The final cube must have a measurement of 3″x 3″ inches on a white piece of Bristol paper.
I first took a white sheet of Bristol and measured a 3″ x 3″ inch square. I then used the model template of a cube I made earlier to construct this one.
Template of a 3″x 3″ inch cube
I used scissors and an Exacto knife to cut out my net. Using the Exacto knife I scored the sides that needed to be folded. [I didn’t want to have the pencil lines show so I flipped to template over and marked each end of a score line with a light dot. Using an Exacto knife I scored and connected the dot marks]
I began folding the template into a cube shape. I apply tacky glue onto the tabs using a small piece of leftover Bristol paper as an applicator. This method helped me to smoothly/ thinly/ and evenly spread the glue onto the tabs. I connected each tab to its matching side (gluing on the inside of the cube) and held the 2 pieces together for about thirty seconds until the glue dried.
I found that it was hard to put some of the pieces together at the corners because the flaps were too big so I had to trim some of them down.
Perfect Cube
We brought the cubes into class for evaluation and my cube was put into the middle category: not perfect and had some flaws.
I noted down some things I could have done to improve my craft for next time:
- Remembering to make the flaps smaller at the corners so they will fit together better
- And surface pencil markings need to be erased
- Needed to find another strategy to make straighter more accurate score lines so that the bristol folds properly
Then in class, together we worked on making a Trapezoidal Prism.
We were given a PDF template of the net and figured out some of the missing measurements using estimation and calculation.
Net for Trapezoidal Prism
Using the template, I drew a grid similar to the one on the PDF onto a piece of Bristol and made the template. Again, I cut out the template and scored on the sides that would need to be folded. This time I scored on top of my pencil markings and erased it after to create straighter score marks. I applied tacky glue onto the tabs using a small piece of leftover Bristol paper as an applicator. I connected each tab to its matching side and held the 2 pieces together for about thirty seconds until the glue dried.
Trapezoidal Prism
Exercise 1b: Building the Icosahedron
I first searched for an icosahedron template.
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Once I found the template I estimated each of the triangles to be equilaterals so I decided to make each side a length of 2 inches. I cut out one 2-inch equilateral triangle on a sheet of Bristol and used it to trace the rest of the triangles.
I cut the template out using scissors and an Xacto knife and glued the sides together.
Icosahedron
Composition #1: Normal Cube
For the final project, I chose to do a cube shape and use the negative space option as my modification.
First I drew the template of my cube. I used the same outline as the first cube made in exercise 1A but instead of having it 3″x 3″ inches, I scaled it so that it could be 4″x 4″ inches so that it could be larger.
4″ x 4″ Cube Template
I used an Exacto knife to cut the corners/ tabs and using scissors to cut the larger straight-edged sides of the cube.
I remembered to make the tabs curved at the corners so that the sides can easily fit together.
This time I scored on top of a light table so I could see my template and not have to worry about the pencil markings showing up on the surface of the cube.
I apply tacky glue onto the tabs using a small piece of leftover Bristol paper as an applicator. I connected each tab to its matching side and held the 2 pieces together for about thirty seconds until the glue dried.
Final Cube Composition
Composition #2: Modified Cube Using Negative Space
Idea #1: Cube with Pyramid Cut Out
First I brainstormed some ideas I could do for the negative space element.
I sketched out some ideas.
Cube Sketches
I wanted to do 6 pyramids cut out of the cube.
First I needed to figure out the measurements of the pyramid. I made the square base of the pyramid 2″x 2″ inches. I knew that the height of the pyramid had to be 1 inch because 2 pyramids must add up to 2 inches since it’s a 2″ x 2″x 2″ cubic inch.
I needed to find the length of the other 2 sides of the triangle. I used the Pythagorean theorem to find the diagonal length of the square and got 2.83 inches. I divided it by 2 to get the length of where the height intersects (1.415 inches). I used the Pythagorean theorem again to find the length of the pyramid and got 1.73269 inches.
Since I got the dimensions of one pyramid, the other 5 pyramids are the same so they just need to be repeated when built.
After that, I drew out the net of the cube.
Designing the Cube with the Pyramids Cut Out
Ideas #2: The Cube Staircase
The other idea I came up with was the cube staircase. I made a 4″x4″ inch cube making a grid on the cube so that each 1″x 1″ inch cube was visible. I colored in the staircase on each side.
I first sketched out a couple of options for where the staircase could be located. After drawing I realized that these designs will not work because the base of each staircase needs to be present. The base of the staircase was positioned at the opening of another staircase which does not make sense.
Cube Sketches that Don’t Work
I fixed this problem and made another design where all the staircases have a base.
I tried making a single net; thinking about what the stairs would look like opened up. I successfully sketched out one side of the cube with one of the staircases.
Net Sketches: Single Net vs Separate Nets
Another option was to make 3 nets of the stairs and attach them to an inside cube. There must be a cube in the center of all the staircases, so I broke down the cube to find out where exactly it would be placed. I made a net for the inside cube and then made a separate net for the small cube in the middle.
I realized that I couldn’t make separate nets of the staircase because the cutouts of the staircase will be seen on the backside of the cube. It should be seamless on the back. I could only make separate nets where the 2 edges connect.
Net of the Inside Cube
Making Cube Composition #2: The Cube Staircase
Part 1:
I decided to go with the staircase design because I thought it was challenging and visually interesting.
First I started sketching out the net of the cube and practiced making the cube on grid paper. I made every 4 grid paper squares as 1 unit. I imagined what the cube would look like opened up and used that to guide my template.
Net on Grid Paper
I decided that it was best to make 3 separate templates.
In the first template, I had the back, bottom, and front side stairs of the cube all attached
For the second template, I had the right-side staircase
And for the last template, I had the top staircase and the left face of the cube together.
Cut them out and began to fold them into the cube.
I taped them down and anything that was missing from the net I added more using separate pieces of grid paper and tape. Using a red marker, I marked where the sides would be connected/ where the tabs would be in the final composition.
Right Side of the Cube
Top and Left side of the Cube
Back, Bottom, and Front of the Cube
After I was able to successfully build the cube. I took it apart and laid it flat to see the finalized net.
On a piece of Bristol, I made a grid with 1″ x 1″ units. I copied the net I made on the grid paper and put it onto my Bristol. I labeled each side.
I decided to make the bottom its separate net so it would be a total of 4 separate nets.
Net of the Cube staircase on Bristol
I cut out all the separate nets using an Exacto knife and scissors making sure to trim the flaps. I used the light table to make my score marks. I used tacky glue and a small piece of Bristol paper as an applicator to spread the glue out evenly and thinly.
I forgot one of the tabs so I made a separate one and glued it in.
I folded at the score lines and began to glue everything together and placing the tiny cube in the middle hole where all the staircases met.
Problems with the Cube
- As I was gluing I ran into problems with the glue mixing with the pencil markings and it would smudge around the edges. Erasing it made it worse spreading the darkened glue.
- I trimmed the tabs a little too much and I started seeing holes and tiny gaps at the corners as I put them together.
- Even though I carefully cut all the lines as straight as I could, I still saw some unevenness and they weren’t lining up properly.
- Since the small cube in the middle was a separate net, I wasn’t able to glue it without making the glue visible and just placing it in, you could see it wasn’t connected to anything. [All of these problems can be visibly seen in the above pictures]
With all these flaws, I couldn’t use it in my final composition because of the poor craft. The staircase cube takes a very long time to make and it was hard to get all the stairs to line up with one another so I last minute changed to my first cube idea. I thought that even though it was an easy design and not as visually interesting as the staircase, the craft might be better at the end.
Iteration and Production:
Making Cube Composition #2: The Cube with the Cut-out Pyramids
First I used the measurements from my first cube idea to make the net. I drew a triangle with the dimensions with calculated dimensions. I cut out the triangle and used it as a template to make the net. I changed the net so that at least one side of the triangle was connected to another side of the triangle. I made a total of 4 nets.
Net of the Pyramids
With this design, I was able to score directly onto the template because the scored side will not be seen. The scored side will be glued to the other pyramids.
I thought it would be interesting to create a pattern on the inside of two of the pyramids. I used a compass to make rings on the inside of the pyramid. I thought it would make it more visually interesting having it be the shape of a cube, with pyramids cut out of them, with a circular pattern on the inside. So I would be using 3 different types of shapes in one composition.
Creating circle pattern in Pyramid
After scoring everything I folded at the score marks and glued the flap to the (outside) side of my pyramid. Once I had my 4 pyramids I began to glue the pyramids together. I remembered to erase all pencil markings before gluing to avoid darkening the glue and accidentally smudging it. I traced the circles with sharpie.
Cube with Cut out Pyramids Built
Problems with the Cube:
- Everything was working until I had to glue the last pyramid. As I was gluing the last pyramid in place and the other sides that were already glued down started popping open and ripping apart.
- The width of the last pyramid could not fit into the last spot even though I measured it properly. Every time I held one side of the cube another side would eventually pop open.
- I realized that I didn’t account for the measurement of the thickness of the glue and the overlapping tabs of Bristol. All of those minor details contributed to the last pyramid not fitting properly. This would have worked with thinner paper but I did not think about how to thick the Bristol was.
Gaps in-between the Pyramids
I decided to start over trying another way to solve this problem.
I made the same net again and cut it out as I did before.
I first glued the first 3 pyramids. I decided to make one extra pyramid to place on one of the sides for more stability. Instead of connecting the last pyramid in I measured out 1 triangle and glued it where the missing pyramid side was.
Reflection
Through this assignment, I have learned to how to translate 2D shapes into 3D shapes. I got to practice making nets/ templates for various polyhedrons. I ran into many different problems in this project through it I have learned to think from different perspectives and I have practiced strengthening my problem-solving skills. I have also learned how to improve my craft for future projects (For example: how to apply glue/ how to cut in straight lines using the knife, using the light table for tracing/ scoring, etc)
Final Product
Composition #1: Original Cube
Composition #2: Negative Space
