Triangle Constructions

Triangle Constructions lesson plan

Who can grasp solid geometry? Make 3-dimensional shapes to manipulate into polyhedra using Color Explosion™ paper.

  • 1.

    When most people study the geometry of three-dimensional space, it is helpful to be able to see, feel, and build the structures. A polyhedron is a 3-D solid that made up of polygons (2-D figures made up of line segments, edges that are connected two at a time at their endpoints) or more simply, flat faces usually joined at their edges.

  • 2.

    For this exercise, students try using a triangle (although other shapes such as squares will work). First, make a template to trace several triangles. Using a ruler, draw an equilateral triangle (3 equal sides, 3 equal angles) on cardboard with Crayola Erasable Colored Pencils. This will be the flat surface building block for the polyhedra.

  • 3.

    On each side of the triangle, extend the edge equally to make three tabs around the triangle as shown in the picture. (When constructing shapes, these tabs will align with tabs of other triangles.) Cut out template with Crayola Scissors.

  • 4.

    Trace the template on white Crayola Color Explosion™ Paper. To get as many triangles per sheet as possible, draw triangles next to each other so they share edges. Start out with at least 12 triangles. Cut out the triangles with scissors. Using Color Explosion™ Markers, decorate each triangle with a unique design.

  • 5.

    Place a ruler along each tab of the cutout triangles. Bend up tab edges.

  • 6.

    Line up the tabs of two triangles and join them together with a rubber band. Students keep adding triangles until they have constructed simple polyhedrons. Students count the number of faces, vertices, and edges to determine what shape was constructed.

  • 7.

    After making regular polyhedra (shapes with equal edge lengths), challenge students to create irregular ones, where the sides and angles are not equal.


  • LA: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade level topics and texts, building on others’ ideas and expressing their own clearly.
  • MATH: Draw, construct and describe geometrical figures and describe the relationships between them.
  • MATH: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
  • VA: Intentionally take advantage of the qualities and characteristics of art media, techniques, and processes to enhance communication of experiences and ideas.
  • VA: Select and use the qualities of structures and functions of art to improve communication of ideas.


  • Encourage students to use the Polyhedral Formula to check on created shapes. The number of faces, plus the number of vertices, minus the number of edges, should equal 2.
  • Students investigate the different types of Polyhedra, such as Platonic solids, prisms, and pyramids. Create an example of the type researched.
  • Students participate n a Polyhedra Scavenger Hunt to locate three-dimensional shapes in everyday life. Locate as many as possible in both the home and school environment. Create a list of findings and document the number of sides in each. Note the use of the item in everyday life.