Answer:
13 vertices. In geometry, the augmented hexagonal prism is one of the Johnson solids (J54). As the name suggests, it can be constructed by augmenting a hexagonal prism by attaching a square pyramid (J1) to one of its equatorial faces. When two or three such pyramids are attached, the result may be a parabiaugmented hexagonal prism, a metabiaugmented hexagonal prism or a triaugmented hexagonal prism. Augmented hexagonal prism.
Type: Johnson J53 - J54 - J55
Faces: 2x2 triangles 1+2x2 squares 2 hexagons
Edges: 22
Vertices: 13