In topology, the dunce hat is a compact topological space formed by taking a solid triangle and gluing all three sides together, with the orientation of one side reversed. Simply gluing two sides oriented in the opposite direction would yield a cone much like the dunce cap, but the gluing of the third side results in identifying the base of the cap with a line joining the base to the point.

Horsmonden is a village in the borough of Tunbridge Wells in Kent, England. The village is located in the Weald of Kent. It is situated on a road leading from Maidstone to Lamberhurst, three miles north of the latter place. The nearest railway station is Paddock Wood.