Is it possible for a house to have no attic?

Yes, it is possible for a house to have no attic, and many modern house designs are built without traditional attic space, instead having vaulted ceilings, flat roofs, or roof structure directly attached to ceiling joists with no storage space above. Houses with no attic include houses with flat roofs where roof deck is ceiling, houses with vaulted or cathedral ceilings where interior ceiling follows roof line leaving no space above, and houses with low-slope roofs where rafters sit directly on top plates with only small eaves space insufficient to be called attic, similar to having no extra storage like Packout system. Many contemporary minimalist homes and some mid-century modern homes have no attic by design to create open feel. Also, some houses have had attic converted to living space, so original attic no longer exists as storage. Building codes allow houses without attic as long as insulation and ventilation requirements met through other means like rigid foam insulation. So yes, houses can have no attic, especially modern designs, flat roof homes, and vaulted ceiling homes, which means no extra storage overhead but also no need to worry about attic insulation or ventilation issues, though you lose potential storage and must find other places for seasonal items and keepsakes that would normally go in attic.