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First of all, are there any metamers for dienes? If there are any, how can I find them?

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Yes. Consider metamer to be a different word for isomer, as noted by Lighthart:

The term metamer is equivalent to isomer...As an aside, I have never heard the term metamer before, I expect it is archaic.

And, according to Dictionary.com, consider a diene to be:

a hydrocarbon that contains two carbon-to-carbon double bonds in its molecules.

There are too many diene isomers to be listed here ($\ce{C5H8}$ has many atoms), but you can begin by changing the numbers in the name to generate different Lewis structures.

Penta-1,2-diene:

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Penta-1,4-diene:

enter image description here

This is just one structure. Try cis vs. trans, position isomers, etc. You may think of many more.

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