Yep, it's the C-57D.
TZ, shot at MGM beginning only three years after
Forbidden Planet was completed there, made repeated use of props, costumes, "Robby The Robot" and even - I believe - landing footage of the spacecraft on several occasions.
"Third From The Sun"
EDIT to add:
I guess I was mistaken about TZ using stock footage of the C-57D landing. Here's an image from the episode in question:
"Death Ship"
The model, repurposed here as "cruiser E-89," has actually been reshot in a
new, custom tabletop landscape. Pretty impressive for early '60s TV!
Interestingly enough, Gene Roddenberry produced his brief TV series
The Lieutenant at MGM and - according to online sources, anyway - initially pitched
Star Trek to them. MGM was a much larger, far more successful film and TV studio in those days than Desilu, and it's entirely possible that had Trek been produced there the producers would have made the same extensive re-use of available props and sets of sophisticated design as
Twilight Zone did.
And that's
Number6's cue to post his cool Photoshop of our gallant crew decked out in the livery of C57-D.
