The house graph is a simple graph on 5 nodes and 6 edges, illustrated above in two embeddings, whose name derives from its resemblance
to a schematic illustration of a house with a roof. It is implemented in the Wolfram
Language as GraphData["HouseGraph"].
The house X-graph is the house graph plus the two edges connecting diagonally opposite vertices of the square base, illustrated above. It is also one of the two graphs
obtained by removing two edges from the pentatope
graph
(the other being the wheel graph). It is implemented in the Wolfram
Language as GraphData["HouseXGraph"].
(the other being the 
wheel graph). It is implemented in the Wolfram
Language as GraphData["HouseXGraph"].
