## BUILD A DODECAHEDRON a micro guide by HowDo Team on HowDo

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## SEE ALSO:

**Build objects from a model or picture**

This is a great way to develop spatial visualization and pattern recognition skills. Check out Polyhedraville, our photo Gallery for models to get you started.

For an extra challenge, try counting how many pieces are required before starting to build your model.

**Build by connecting**

Two objects that contain a same-shaped piece can be joined by removing that piece from each and then connecting the freed notches. The picture shows two dodecahedra (red and yellow) and a pentagonal prism (blue). They are connected by common pentagonal faces.

*Hint: When building objects to connect, make sure you build each object with the notches pointing in the same direction. If the notches are facing the opposite way, you will have to reconstruct one of the objects!*

**Build by connecting, part 2.**The model at right can be build as follows:

- Build a dodecahedron
- Connect, as described above, 12 pentagonal pyramids to the 12 faces of the dodecahedron
- Connect a tetrahedron to each triangular face of each pentagonal pyramid

*Hint: Note that the faces of the original dodecahedron and of all the pentagonal pyramids have been removed in the final object. It is much easier to build this model directly using 180 triangles, without any connection steps, but the best way to describe is still in terms of simpler components and*

*connections between them.*

**Build from description**

- Build a polyhedron that has only square faces and hexagonal faces and has the following properties: (a) each square has only hexagonal faces as neighbors, and (b) each hexagonal face has three square and three hexagonal neighbors that alternate.

*Hint: The polyhedron has 6 squares and 8 hexagons.*

*Answer: truncated octahedron*

- Build the object obtained by replacing every face of a cube with a square prism without the base.

**Build from description game**for two-players teams: one team member looks at an object (or a picture of an object) and describes it to the other team member who must build it. The team get points if the built object matches the original one.

**Build with colors**

- For a given object, what is the minimum number of colors needed so that no two same-colored faces touch each other along an edge?

*Answer: tetrahedron: 4, cube: 3, octahedron: 2, dodecahedron: 4, icosahedron: 3, cuboctahedron: 2, truncated tetrahedron: 4, truncated octahedron: 3, etc.*

- What if two faces of the same color are not allowed to touch even at a vertex?

*Answer: tetrahedron: 4, cube: 3, octahedron: 4, dodecahedron: 4, icosahedron: 5, cuboctahedron: 5, truncated tetrahedron: 4, truncated octahedron: 3, etc.*

- For a given object, how many faces of the same color can you place so that they do not touch each other at an edge/corner?

*Answer: tetrahedron: 1/1, cube: 2/2, octahedron: 4/2, dodecahedron: 3/3, icosahedron: 8/4, cuboctahedron: 8/4, truncated tetrahedron: 4/4, truncated: octahedron: 6/6, etc.*

**Build from net**

- Build an object given its net (see picture at right).

*Answer: tridiminished icosahedron.*

**Net puzzle**

- Which figure at far right is a net of the triangular prism?

*Answer: B.*

**Build with no rules.**Bend and twist the ITSPHUN pieces to connect them in ways they were not meant to be connected!

- Build the model at right

*Hint:*

*reverse the w*

*eave of the bottom (hidden) hemisphere.*

- Find new ways to play with ITSPHUN (and send us some pictures).

*Suggestion: see a few examples in our photo gallery. The star-shaped pieces might offer more possibilities to be creative.*