There's Polyhedra Hanging from the Ceiling
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On the last day before Christmas vacation, my class constructs different polyhedra. We trace the templates onto poster board using a different color for each type of polygon. Students autograph several polygons. These polygons are stapled together into polyhedra and hung from the ceiling with string. We use templates made from file folders. Each regular polygon has sides of 2 inches. |
List of polyhedra and polygon requirements
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Polyhedra |
Polygons needed |
Construction tips |
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Regular polyhedra |
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tetrahedron |
4 triangles |
3 triangles meet at each vertex |
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hexahedron |
6 squares |
3 squares meet at each vertex |
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octahedron |
8 triangles |
4 triangles meet at each vertex |
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dodecahedron |
12 pentagons |
3 pentagons meet at each vertex |
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icosahedron |
20 triangles |
5 triangles meet at each vertex |
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Semiregular polyhedra |
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truncated tetrahedron |
4 triangles 4 hexagons |
2 hexagons and 1 triangle meet at each vertex |
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truncated hexahedron |
6 octagons 8 triangles |
2 octagons and 1 triangles meet at each vertex |
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truncated octahedron |
6 squares 8 hexagons |
2 hexagons and 1 square meet at each vertex |
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truncated dodecahedron |
12 decagons 20 triangles |
2 decagons and 1 triangle meet at each vertex |
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trancated icosahedron |
20 hexagons 10 pentagons |
2 hexagons and 1 pentagon meet at each vertex |
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cuboctahedron |
6 squares 8 triangles |
2 squares and 2 triangles meet at each vertex |
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rhombicuboctahedron |
8 triangles 18 squares |
3 squares and 1 triangle meet at each vertex |
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rhombitruncated cuboctahedron |
10 squares 8 hexagons 6 octagons |
1 octagon, 1 hexagon and 1 square meet at each vertex |
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snub cuboctahedron |
6 squares 32 triangles |
1 square and 4 triangles meet at each vertex |
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icosidodecahedron |
12 pentagons 20 triangles |
2 pentagons and 2 triangles with the triangles attached to the sides of the pentagons |
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rhombicosidodecahedron |
12 pentagons 20 triangles 20 squares |
1 pentagon, 2 squares and 1 triangle meet at each vertex with the squares attached to the sides on the pentagon and the triangle in between, attached to the squares |
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rhombitruncated icosidodecahedron |
12 decagons 30 squares 20 hexagons |
1 decagon, 1 hexagon and 1 square meet at each vertex (this one is huge!) |
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snub icosidodecahedron |
12 pentagons lots of triangles |
1 pentagon and 4 triangles meet at each vertex |
Note: numbers on the more complex polyhedra are approximate (students counted these.)