Shape Skeletons
Creating Polyhedra with Straws
Topics: 3-Dimensional
Shapes, Regular Solids,
Geometry
Materials List
 Drinking straws or
stir straws, cut in
half
 Paperclips to use
with the drinking
straws or chenille
stems to use with
the stir straws
 Scissors
 Appropriate tool for
cutting the wire in
the chenille stems,
if used
Use simple materials to investigate regular or advanced 3-dimensional shapes.
Fun to create, these shapes make wonderful showpieces and learning tools!
Assembly
1. Choose which shape to construct. Note: the 4-sided tetrahedron, 8-sided
octahedron, and 20-sided icosahedron have triangular faces and will form sturdier
skeletal shapes. The 6-sided cube with square faces and the 12-sided
dodecahedron with pentagonal faces will be less sturdy. See the Taking it
Further section.
Platonic Solids
This activity can be used
to teach:
Common Core Math
Standards:
 Angles and volume
and measurement
(Measurement &
Data, Grade 4, 5, 6, &
7; Grade 5, 3, 4, & 5)
 2-Dimensional and 3Dimensional Shapes
(Geometry, Grades 212)
 Problem Solving and
Reasoning
(Mathematical
Practices Grades 212)
Tetrahedron
Cube
Octahedron
Polyhedron
Faces Shape of Face
Tetrahedron
4
Triangles
Cube
6
Squares
Octahedron
8
Triangles
Dodecahedron
12
Pentagons
Icosahedron
20
Triangles
Dodecahedron
Icosahedron
Edges Vertices
6
4
12
8
12
6
30
20
30
12
2. Use the table and images above to construct the selected shape by creating one or
more face shapes and then add straws or join shapes at each of the vertices:
a. For drinking straws and paperclips: Bend the
paperclips so that the 2 loops form a “V” or “L”
shape as needed, widen the narrower loop and insert
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 3dimensions, 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
Shape Skeletons, page 2
Stellated Octahedron
Stellated Octahedron
Copyright 2014, RAFT