Modeling products with completely different sets of necessary information and their linking to lines?

I am currently working on a site that sells custom-made products of various types. I have a common standard basket diagram: the order has a lot of linear elements, LineItems has one product, but I ran into some problem:

Let's say that one of our products is a ball, and one of our products is a box of crayons. While people create their order, we create elements that can be represented by some psuedocode:

Ball:
  attributes:
     diameter: decimal
     color: foreign_ref_to Colors.id
     material: foreign_ref to Materials.id
CrayonBox:
  attributes:
     width: decimal
     height: decimal
     front_text: string
     crayons: many_to_many with Crayon
...

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LineItem
  information: many_to_many with product_information
  ...
ProductInformation:
  lineitem: many_to_many with line_item
  name: string
  value: string

ProductInformation(name='color', value=$SOMECOLOR)
ProductInformation(name='color', value=$SOMEOTHERCOLOR)
...

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