(defparameter *segments*
  '((p0 (p1) (p2 p4 p6) (p3 p7 p9) (p5 p8 p10))
    (p1 (p2 p3 p5) (p4 p7 p8) (p6 p9 p10))
    (p2 (p3 p5) (p4 p6))
    (p3 (p5) (p7 p9))
    (p4 (p7 p8) (p6))
    (p5 (p8 p10))
    (p6 (p9 p10))
    (p7 (p8) (p9))
    (p8 (p10))
    (p9 (p10))
    (p10)))

;; A dynamic variable to hold to final solution
(defvar *triangles*)

;; Removes sub-lists from a list (eg, (a (b) c) => (a b c)
(defun explode (object)
  (when object (if (listp object)
                   (append (explode (car object)) (explode (cdr object)))
                 (list object))))

;; Loops from a given point over all the possible connections to it
(defun map-segments (p1 rest)
  (let ((links (explode rest)))
    (loop for segment in rest collect
          ; gather all the sub points along a segment
          (loop for p2 in segment do
                ; find all the points connected to p2 from the list
                (loop for p3 in (explode (cdr (assoc p2 segments))) collect
                      ; only connect p1->p2->p3 if p1 can reach p3
                      ; and p2->p3 are not on the same line segment
                      (when (and (not (member p3 segment)) (member p3 links))
                        (push (list p1 p2 p3) *triangles*)))))))

;; Sets the global return value and calls map-segment once for each point
(defun find-triangles ()
  (let ((*triangles* nil))
    (loop for connections in *segments* do
          (map-segments (first connections) (rest connections)))
    ; return the final list of all triangles found
    (reverse *triangles*)))