; Naming lines:
; A (bottom)
; B C D (from left corner, excpt bottom)
; E F G (from right corner, excpt bottom)
; All triangles will start with non-bottom left-corner lines: (B C D)
; Second line: any right-corner non-bottom line: (E F G)
; Third line: Any line except the first and second.
; Collect triangle unless an equal triangle is already listed

(let (all)
   (labels
    ((tri-eql (a b) (null (set-difference a b))))
    (dolist (s1 '(b c d))
      (dolist (s2 '(e f g))
        (dolist (s3 '(a b c d e f g))
          (let ((tri (list s1 s2 s3)))
            (unless (or (eq s1 s3) (eq s2 s3)
                        (find tri all :test #'tri-eql))
              (push tri all)))))))
   (print (length all)))