Therefore it isn't possible to make a solid with six equilateral triangles at each vertex. Six angles of 60 ° add to 360 ° which is a full turn and is "flat" when joined. The internal angles of an equilateral triangle all measure 60 °. Surrounding a vertex with six triangles creates a tessellation which covers a plane, or flat surface. Is it possible to put six triangles around each vertex and make a solid? Three triangles surround each vertex of the tetrahedron, four triangles for the octahedron and five for the icosahedron. Look carefully at each vertex of the three polyhedra we have made from triangles.įocus the discussion on the consistent pattern around each vertex. If a student has created an icosahedron (icosa- means twenty), draw the student's attention to it. Point out that regular polyhedra are named by the number of faces.ĭoes anyone have a different polyhedron made only from triangles? The solid on the right is called an octahedron. The solid on the left is called a tetrahedron. What is the same about these two solids? (made only of triangles) After a suitable collection has developed, bring the class together. If needed, go back to the example of the soccer ball to provide an example of symmetric balanced solid.Īllow the students time to build the solids. How many different solids can you make only using equilateral triangles or squares? Let's try to build solids that look balanced. How many vertices does a cube have? (eight) top and bottom, four faces around the middle.)Įxplain that the corners can be called vertices. How can you count the faces to check you count them all? (e.g. How many of those shapes are needed? (six) What is this solid shape called? (a cube) Show students a cube you have constructed from plastic polygons (polydrons, geoshapes, etc.) or card (see below). How many of each shape meet at one vertex? Is that combination the same for each vertex? (Two hexagons and one pentagon meet at each vertex.) What shapes can you see? (Pentagons and hexagons)
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