Joan wore this gown in episode 114 of season 5 "The Heiress" and in episode 154 of season 7 "The Choice".
In season 5 Alexis wears this gown in a scene with King Galen while visiting Moldavia. King Galen is in pursuit of Alexis, while she passively resists. In season 7 Alexis wears this gown while crashing a Carrington family dinner at The Carlton hotel, with Zach Powers as her date, and also later in a scene with Blake in the hotel lobby.
This gown is pink fabric with silver metallic bugle beads, with different sized round crystals scattered through out, as well as rhinestone floral embellishments by the sleeve line. The sleeves are taffeta with lines of silver bugle beads with half inch to one inch spacing and scattered round rhinestones, as well as a rhinestone floral embellishment in the middle of the bow like sleeve. The beading is in a "sun burst" pattern starting at the right side of the waist and spraying outwards in all directions, as stated on the sketch. The gown has a center slit that follows the sun burst pattern of the beading. The gown also has a built-in corset, which was a special feature Nolan was known for. Joan doesn't get full credit for that tiny waist!
The gown was altered for its second appearance on the show. The taffeta shoulder wrap sleeve was transformed into two large bow-like sleeves on either shoulder. A crystal embellishment was removed from the waist where the beading and crystal pattern begins, and more crystal embellishments were added in between the "bow" sleeves and also to the back of the gown.