Embodiments of the present invention provide methods and equipment for automatically assembling three panes of glass and corresponding spacers so that air or other gas can be injected into the two between-pane spaces. The equipment can receive two glass panes that each have spacers coupled to one of their major surfaces, along with a third glass pane having no spacer coupled to its major surfaces, and can assemble the three glass panes into a “teepee” configuration in which the two spacers each contact two of the glass panes along a common edge of the glass panes. Preferred equipment can receive a glass pane in a first orientation and rotate the glass pane 180° to a second orientation in which the glass pane's two major surfaces face opposite directions from the first orientation. Such preferred equipment can then receive a two-pane teepee from a previous piece of equipment and can add the “flipped” single glass pane to the teepee to create a three-pane teepee.