Paper Folding - Models of the Platonic Solids
Here are some simple recipes for building models of the Platonic solids out of paper. I use A4 paper - that is rectangular paper such that the length of the long side of the rectangle divided by the length of the short side is equal to the square-root of 2. The dodecahedron and icosahedron models have appeared previously on the NRICH web-site. Jul 24, · Templates are in the book Amazing Math Projects You Can Build Yourself odishahaalchaal.com
In this project, learn a simple technique based on circles for making all five Platonic solids—tetrahedron, octahedron, icosahedron, cube, and dodecahedron. The solids also make nifty boxes, fun decorations and unique calendars—special patterns included! Each solid is made from a what is scentsy wax made of, with the shape the solid is based on drawn inside of the circle.
This construction technique reinforces the concepts of Platonic solids as the student assembles each solid. Three-dimensional objects with only flat or plane surfaces are known as polyhedra. There are many different polyhedra, but five of them have the property of being regular, or "Platonic". A solid is regular if all planes or faces are the same, and the same number of planes meet at each corner or vertex.
Five solids qualify as regular: three are based on equilateral triangles tetrahedron, octahedron, and icosahedronone is based on ppaper cubeand one is based on regular pentagons dodecahedron. Papdr craft: For other platonkc solids to make, see the project Geometric Solids. Choose the platonic solid you want to make—there are templates for triangle, square and pentagon faces. For the cube, print squares; for the dodecahedron, print pentagons, and print triangles for the tetrahedron, octahedron and icosahedron 2 sheets.
Download and print the pattern on paper or cardstock. The patterns are available in color or in black and white, for you to print on colored paper or add your own design. Patterns are Adobe PDF files. The Adobe Reader is available for free. All of Aunt Annie's project patterns are designed to be printed on standard letter-size paper 8. Fold on each of the three or four or five fold lines.
To hide the printed fold lines, turn the circle with the printed side down before folding; otherwise, keep the printed side up. Repeat for each circle. For circles printed on cardstock, score the fold lines first with the empty ballpoint pen. How to write a reference letter for a teacher You may optionally decorate the inner triangles, squares, or pentagons with crayons, markers, stickers, or rubber stamps.
Decorate on the unprinted side. Icosahedron only: Glue ten folded circles with triangles into a ring using the maake tabs. Tip: If you want, the glue tabs can be folded down and glued to a face or trimmed to one-eighth of an inch. That's it! Your Platonic solids aolids complete! Tip: Make a plaonic in the form of a dodecahedron. Print the calendar pattern or calendar pattern hpw paper or cardstock and platonix following the instructions in this project.
For more creativity, you might print the black and white calendar patterns see Step 1 on white or pastel colored cardstock and decorate it with markers in any way you like! Tip: Make decorations or boxes for the Fourth of July using the Stars and Stripes pattern to makd tetrahedron, jow and icosahedron!
Light up any patriotic holiday with tetrahedron covers for string lights. Tip: These solids can be used as gift boxes. Print directly on cardstock. Decide how you want the box to open and leave tabs unglued as needed for paepr lid. Tip: The bottom halves of the dodecahedron and icosahedron can be used as bowls for party decorations. Witj The bottom of sopids dodecahedron filled with paper flowers attached to a balloon. See a sample newsletter. Project Index Downloads.
Aunt Annie's Crafts Craft projects and more! Search auntannie. Loading search Computer paper or cardstock, plain or colored Optional: Empty ballpoint pen and ruler, markers, crayons, stickers. Glue or double-sided tape Scissors.
Share this craft with friends and family. Before you start Make a place to work. Read all of the directions. Gather everything you need to do the project.
Think about the project. Imagine how it will look and what you will do with it. How to Make Platonic Solids Read maje of the steps before starting. Step 1: Choose a Pattern and Print It Choose the platonic solid you want to make—there are templates for triangle, square and pentagon what are high risk investments. Search AuntAnnie.
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Introduction: CMY Paper Platonic Solids
if you want to hang your platonian solids from the ceeling like i did, attach a white or nylon thread (that way it will be almost invisible) to one corner of your solid with a needle. make a knot. since the shape weighs so little, you can just glue the other end of the string to the ceeling with some clear tape. as the light shines through, you can see how cyan and magenta make violet, magenta and yellow make Estimated Reading Time: 4 mins. Nov 13, · Jamie York gives a lecture explaining how to construct Platonic solid models from paper. Apr 11, · The video shows the five Platonic solids: Icosahedron (20 faces)- Dodecahedron (12 faces)- Octahedron (8 faces)- Cube (6 faces)- Tetrahedron (4 faces)For ne.
This article describes how to build models of the Platonic solids using sheets of paper. Suppose you have a collection of regular polygons and each polygon has the same number of faces.
For example, the polygons may all be regular squares. Connect the polygons together edge to edge to form a structure like a shell which completely encloses a region. For example, six regular squares can be connected together to form a cube. Such a structure is known as a polyhedron. The polyhedron is regular if, informally speaking, it has as much symmetry as possible.
To appreciate better what regular means, position the polyhedron in front of you so that you are directly facing a vertex, and take a photograph.
Adjust the polyhedron so that you face a different vertex and take another photograph. The polyhedron is regular if, after rotating the photographs suitably, the images in the two photographs appear identical, no matter the choice of vertices. There are exactly five such regular polyhedra shown below , and they are known as the Platonic solids. Here are some simple recipes for building models of the Platonic solids out of paper.
I use A4 paper - that is rectangular paper such that the length of the long side of the rectangle divided by the length of the short side is equal to the square-root of 2.
For the purposes of illustration, the pieces of A4 paper used below are coloured red on one side and blue on the other. The tetrahedron. Fold an A4 sheet of paper as shown below. The result is a tetrahedron net, but it will not maintain the shape of a tetrahedron of its own accord. Make another identical net, then slot the two nets together to form a rigid tetrahedron.
The octahedron. Make four tetrahedron nets following the recipe above for each one. Slot them together to form an octahedron. To do this, slot two nets together to form what looks like a square pyramid with flaps attached. Do the same for the other two nets. Now slot these two square pyramid objects together. The cube. This model only truly represents a cube if the ratio of the short to long sides of your rectangular piece of paper is You can achieve this ratio by removing a 17mm width strip from a sheet of A4 paper to decrease the length of the longer edge of the A4 paper.
Repeat the procedure shown below for three separate sheets of paper, and interlock the resulting three objects to form a cube. The object that results from this recipe is a nearly regular pentagon with two flaps. Make twelve of these objects and join them together by the flaps to form a dodecahedron. The icosahedron. We continue from the final stage of the tetrahedron recipe to produce a truncated tetrahedron, shown below.
Make twenty of these truncated tetrahedra and glue them together to form an icosahedron. Excessively dark photographs taken by Kurt Falk. Main menu Search. Paper Folding - Models of the Platonic Solids. The dodecahedron. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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