Machine learning algorithms for Geometrical objects shapes identification
This is quite doable.
Just make sure of the following:

Any test data should be one of the shapes you have trained on.
Make sure you have balanced data. (You can introduce bias if required)
To make it more challenging you can create or find data like google street view images for numbers.
Segmentation and Classification, both are possible.

VGG should do just fine, you could also use resnet. The overall model can be fit into an inventory pipeline where you sort the inventory through shapes!