Shape Skeletons Creating Polyhedra with Straws

Topics: 3-Dimensional Shapes, Regular Solids, Geometry

Materials List  Drinking straws or

stir straws, cut in Use simple materials to investigate regular or advanced 3-dimensional shapes. half Fun to create, these shapes make wonderful showpieces and learning tools!  Paperclips to use

with the drinking Assembly straws or chenille 1. Choose which shape to construct. Note: the 4-sided tetrahedron, 8-sided stems to use with octahedron, and 20-sided icosahedron have triangular faces and will form sturdier the stir straws skeletal shapes. The 6-sided cube with square faces and the 12-sided  Scissors dodecahedron with pentagonal faces will be less sturdy. See the Taking it  Appropriate tool for Further section. cutting the wire in

the chenille stems, Platonic Solids if used

This activity can be used to teach:

Common Core Math Tetrahedron Cube Octahedron Dodecahedron Icosahedron Standards:  Angles and volume Polyhedron Faces Shape of Face Edges Vertices and measurement Tetrahedron 4 Triangles 6 4 (Measurement & Cube 6 Squares 12 8 Data, Grade 4, 5, 6, & Octahedron 8 Triangles 12 6 7; Grade 5, 3, 4, & 5) Dodecahedron 12 Pentagons 30 20  2-Dimensional and 3- Dimensional Shapes Icosahedron 20 Triangles 30 12 (Geometry, Grades 2- 12) 2. Use the table and images above to construct the selected shape by creating one or  Problem Solving and more face shapes and then add straws or join shapes at each of the vertices: Reasoning a. For drinking straws and paperclips: Bend the (Mathematical paperclips so that the 2 loops form a “V” or “L” Practices Grades 2- shape as needed, widen the narrower loop and insert 12) one loop into the end of one straw half, and the other loop into another straw half.

b. For stir straws and chenille stems: Thread whole or cut pieces of chenille stems through straw halves, bending as needed to join the straws together.

Instructions by RAFT Education Department; illustrations by Jay Gluckman (RAFT) Copyright 2014, RAFT The Math Behind the Activity Geometry has ancient roots. The Egyptians excelled at both 2-dimensional and 3-dimensional geometry, and the Greeks connected the solid shapes to both the natural and spiritual worlds. The most basic solid shapes are the “Platonic” and “Archimedean” solids. The five Platonic solids have faces of regular polygons, of equal size and shape, and they have identical vertices. The Archimedean solids are composed of two or more regular polygons.

Students learn a bit more about shapes each school year, starting with describing the faces of solid shapes, then adding measurement of edges, angles, volumes, and surface areas. This activity can be useful at many levels, depending on the needs and abilities of the students.

Taking it Further  Create cube and dodecahedron skeletal shapes out of straws. Determine what kinds of added supports or reinforcements are needed to make a more rigid skeletal shape.  Create a triangular dipyramid - a 6-sided polyhedra with 3 triangular faces on top and 3 on the bottom, 9 edges, and 5 vertices. Create a pentagonal dipyramid - a 10-sided polyhedra with 5 triangular faces on top and 5 on the bottom, 15 edges, and 7 vertices. Compare these polyhedra to the Platonic solids - what are the similarities and differences?  Create stellated straw polyhedra. Stellations are projections from the vertices, edges, or sides of shapes done in a systematic way so that a new shape is created. For example, in 2-dimensions a stellated pentagon is a 5-pointed star or pentagram and a stellated hexagon is a hexagram or 6-pointed star. Stellated shapes are more star-like in appearance and for 3- dimensions will make a more impressive showpiece! In 3- dimensions, each triangular face can have a tetrahedral shape added by connecting a tripod of three straws to each face. In a similar way four straws could be added to each 4-sided face of a cube and five straws added to each 5-sided face of a dodecahedron. Triangular Dipyramid

Web Resources (Visit www.raft.net/raft-idea?isid=495 for more resources!)  Detailed descriptions of 3-dimensional shapes (including formulas), along with links to paper model plans, can be found at “Sacred Geometry” http://www.geometrycode.com/sg/polyhedra.shtml  Teacher designed math courses from the New Jersey Center for Teaching & Learning – https://njctl.org/courses/math

Tetrahedron Stellated Octahedron Shape Skeletons, page 2 Stellated Octahedron Copyright 2014, RAFT