"Only an energy-efficient, resource-efficient design could work for everyone," - R. Buckminster Fuller
There are two reasons domes are energy efficient. The ambient airflow inside the dome is continuous, with no stagnant corners, requiring less energy to circulate air and maintain even temperatures. The energy required to heat and cool a dome is approximately 30% less than a conventional building. The second is the high volume-to-surface-area ratio, requiring less building materials to enclose more space. The lower the ratio of a building's outside perimeter to its enclosed living area, the less energy is required for building, heating and cooling.
The sphere has 25% less surface area per volume enclosed than any other shape. The dome combines the inherent stability of triangles with the advantageous volume-to-surface-area ratio of a sphere. The larger the dome, the more efficient it becomes. This is demonstrated by doubling the diameter, which encloses eight times the volume.