Explorations in Euler’s formula

In our explorations with the relationship between the vertices, edges and faces of a 3D solid, as a part of the Creative Math Program, Jason made a dodecahedron.

We looked at many shapes and solids, and observed the following Euler’s identity hold true for all of them.

V – E + F = 2

Next, The task was to draw or create your own 3D solids and try to verify the Euler’s formula for 3D shapes which talks about the relationship between the vertices, edges and faces of any 3D shape.

Jason made this 12-faced regular 3D solid with beads and connectors.

So, this dodecahedron has 20 Vertices, 30 Edges and 12 Faces, which satisfies the relationship.

Connections to Biology: The alveoli are dodecahedron shaped. Alveoli are tiny air sacs in the lungs where exchange of oxygen and carbon dioxide between the lungs and the blood stream happen.

Will keep updating this page with more explorations by children.

The Creative Math Program is open for for all children of Ages 8 and above.

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