Existence of Regular Space which is not Tychonoff

Theorem
There exists at least one example of a topological space which is a regular space, but is not also a Tychonoff space.

Proof
Let $T$ be a Tychonoff corkscrew.

From Tychonoff Corkscrew is Regular, $T$ is a regular space.

From Tychonoff Corkscrew is not Completely Regular, $T$ is not a Tychonoff space.

Hence the result.