Stellated Rhombic Dodecahedron Project
Create a shape (stellated rhombic dodecahedron) that will flip into a cube.
This creative manipulative will bring geometry to life. Assemble square-based pyramids to create an interactive stellated, rhombic dodecahedron. Find the surface area, volume, and the sum of the angles for each pyramid. Determine the surface area and volume of the dodecahedron.
Assemble nets for cones, cylindars, cubes and rectangular prisms for surface area and volume. Challenge students to create dimensional shapes by combining various solids to think outside the box!
Students create an intricate shape from a square-based pyramid, to learn geometry, problem solving, or plain math fun!
Supplies Used: Construction Paper, Double-Sided Tape, Packing Tape
The teacher will die-cut the materials for student use prior to the lesson.
- Die-cut twenty-four square based pyramids from construction paper or cardstock. Laminating the paper before cutting will make a longer lasting project.
- Fold on the perforations and build twenty-four pyramids using glue or double-sided tape on the tabs (Figure A).
- Create eight pods of 3 pyramids each with the top tips together. Reinforce all of the seams with packing tape. Regular tape will break with repeated bending.
- Arrange the pods in two groups of four with the square pyramid bases flat on the table and flat around the four edges. Tape the two opposite sides (top to bottom) on each group of four (Figure B).
- Pick up two of the pods that have been taped together. Invert or open the seam so that the opposite side of the same (taped) joint is exposed. Tape this (top to bottom) as well. It is recommended to go back and put a second layer of tape on both sides of this seam to reinforce the connection. Repeat this procedure with the remaining three sections of pods.
- Turn the two sets of four pyramid pods over so their bases are on top and flat around the four edges. Each set of four pods has now been taped so eight pods are connected. Now connect the two eight pod sets by taping the pods together on their bases (Figure C). This base seam DOES NOT continue around to the seam already reinforced, it hooks the four pods together. Again, invert or open the seams and reinforce the opposite sides. Go back and put a second tape layer on both sides of these two seams.
- Turn over again, with the bases down, and tape the two groups together in the center (Figure D). Turn and tape the inside of these edges (the 7th and 8th connections). The completed project will be secured in eight places. Again, it is recommended to put a second layer of packing tape (from one end of the seam to the other) on both sides of each joint.
- The pyramids should now flip into many configurations including a cube and a stellated rhombic dodecahedron (see Main Photo).
- Figure A
- Figure B
- Figure C
- Figure D
Mathematics, Grade 6: Geometry
6.G 4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Pre-K-5: Instructional programs from Pre-Kindergarten through grade 12 should enable all students to use visualization, spatial reasoning and geometric modeling to solve problems.
- In Pre-Kindergarten through grade 2, all students should recognize and represent shapes from different perspectives.
- In grades 3-5, all students should identify and build a three-dimensional object from two-dimensional representations of that object.
Standards are listed with permission from Principles and Standards for School Mathematics, copyright 2000 by the National Council of Teachers of Mathematics (NCTM). NCTM does not endorse the content or validity of these alignments.