![]() ![]() Repeat the procedure shown below for three separate sheets of paper, and interlock the resulting three objects to form a cube. 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. This model only truly represents a cube if the ratio of the short to long sides of your rectangular piece of paper is 3:4. Now slot these two square pyramid objects together.) (To do this, slot two nets together to form what looks like a square pyramid with flaps attached. Slot them together to form an octahedron. Make four tetrahedron nets following the recipe above for each one. Make another identical net, then slot the two nets together to form a rigid tetrahedron. The result is a tetrahedron net, but it will not maintain the shape of a tetrahedron of its own accord. The dodecahedron and icosahedron models have appeared previously on the NRICH web-site.įor the purposes of illustration, the pieces of A4 paper used below are coloured red on one side and blue on the other.įold an A4 sheet of paper as shown below. 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. Here are some simple recipes for building models of the Platonic solids out of paper. There are exactly five such regular polyhedra (shown below), and they are known as the Platonic solids. The polyhedron is regular if, after rotating the photographs suitably, the images in the two photographs appear identical, no matter the choice of vertices. Adjust the polyhedron so that you face a different 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. The polyhedron is regular if, informally speaking, it has as much symmetry as possible. Such a structure is known as a polyhedron. For example, six regular squares can be connected together to form a cube. Connect the polygons together edge to edge to form a structure like a shell which completely encloses a region. For example, the polygons may all be regular squares. Suppose you have a collection of regular polygons and each polygon has the same number of faces. Examine your models to see these properties.This article describes how to build models of the Platonic solids using sheets of paper. Four triangles meet at each corner of an octahedron,Īnd five triangles meet at each corner of an icosahedron. Has three triangles that meet at each corner (or vertex). The tetrahedron hasįour sides (or faces), while the octahedron has eight and the icosahedron has twenty. Octahedron net with tabs Octahedron net without tabs PDF version Printable Nets - Dodecahedron Dodecahedrons are polyhedra with 12 faces. Three of the solids in this project are based on equilateral triangles. You can also make an octahedron by sticking two square-based pyramids together. Icosahedron), one is based on squares (cube), and one is based on regular Platonic)-three are based on triangles (tetrahedron, octahedron, and Five solids qualify as regular (also known as A solid is regular ifĪll of its faces are the same, and the same number of planes (faces) meet atĮach corner (vertex). ![]() There are many different polyhedra, butįive of them have the property of being "regular". Solids with only flat surfaces and straight Geometric solids are three-dimensional objects like Keep up with Aunt Annie's Crafts on Facebook , The solid will look neater with the tabs glued on the inside. It is much easier to glue the tabs on the outside, but Outside where the sides meet, or on the inside. Gently form the solid into its shape, referring to the illustration Step 5: Foldīe sure that all folds are sharp. Use a ruler and the empty ballpoint pen (or bone folder) to make an To score: Turn the template with the printed/decorated side up. The fold lines are marked in blue on the illustration. Scoring the fold lines makes for easier folding and sharperĬreases. Pattern have two templates-small and large.) Step 4: Score Step 3: CutĬut around the polyhedron's pattern on the outline. ![]() ![]() Step 2: Color Pattern (optional)Ĭolor the pattern template as you like with markers, colored pencils orĬrayons. When printing from Adobe Reader, you may need to select Auto-Rotate and Center or Choose paper source by PDF page size to ensure the best fit. All of Aunt Annie's project patterns are designed to be printed on standard letter-size paper (8.5"x11" or A4). ![]()
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