Figuring it's never too early to start our baby daughter's mathematical education, my wife and I have been trying to use proper geometric terms for her toys. "Put the ______ in the bucket!" works just fine for "cube", "cylinder", and "triangular prism", but then we've got these shapes:

mystery shapes in three dimensions

mystery shapes straight on

These baffle the both of us, and google is proving unhelpful. The orange shape feels like a "star prism", given it has two bases and an obvious star projection in two dimensions when viewed base-on, but we aren't sure. We've no idea on the purple shape. In purple's case, it's not even clear it's actually a polygon. Unlike the other shapes, where edge curvature looks to be a byproduct of molding, purple has an obvious arc to some of its faces.

So, what are these things? What can we tell our daughter to put back in the toy chest?


(Caveat: I cannot claim any expertise in educating toddlers.)

My hunch is that at this stage instilling meaning matters more than the right terminology. Prism is correct, but speaking about "triangle prism", "star prism", "cross prism" would make her wonder why we do not say "square prism".

I would recommend to teach her the difference between a 2-dimensional shape (square, star, cross) and its 3D-extrusion called prism. Then use names with "cross", "square", etc. as shortcuts.

As an aside, you may like to toss her a challenge: is a cylinder a "prism"? if she say "yes", I would praise her intuition: unless you know what a polygon is, a cylinder looks and feels as a "circle prism". If you ask her to explain why, she might come up with the wonderfully intuitive answer that "a prism is something that never changes its 2d-shape".

Once she gets this (technically incorrect, but meaningful) notion of "prisms" right, start discussing different 3d-shapes. E.g., a "sphere" is not a prism because it gets fatter and thinner along the way.


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