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there is no such thing as a thamnophis radix
Garter snakes are in the genus 'Thamnophis'.
The common garter snake is 'Thamnophis sirtalis'
You have it right in your question, the genus is Thamnophis, and the species is sirtalis. The common name is the garter snake.
Thamnophis
The genus for a Garter snake is 'Thamnophis'