What are the fundamental roots of modern symmetric encryption? In academic pursuits, we often have people (and their ideas) who are considered fundamental to the subject, such as Bayes and probability.
In cryptography, it's obvious to see that the Diffie-Hellman problem is fundamental to modern key exchange algorithms.
Can modern day symmetric encryption methods be similarly traced back to particular fundamental roots or building-blocks? If so, what are they?
Is there a common grandparent (or few) that most modern symmetric crypto such as AES or ChaCha can be undeniability related to?
There are a few here.

Block ciphers like DES and its modes are based of Feistel Cipher, AES is based on Rijndael.

Others like FOX64 based on Lai-Massey scheme.

Other are are stream ciphers like RC4.


So, These are some of the schemes which are used in todays symmetric key ciphers.