How to build a house which faces to both North and South only, but not other directions such as East and West and North East?
You could argue that the following house works:
whether anyone would let you build it is another question
in case it isn't clear from the picture, the 'outside' wall faces north everywhere since it faces away from the south pole, and the 'inside' wall faces south everywhere since it faces towards the south pole.
You could simply
Make it hexagonal. Orient it so that one wall faces north, and one south. The Others will face NE, NW, SE, SW. None face due east or west.
Note: The question has been edited. This answer satisfied the original conditions but is no longer valid.
With the new conditions, it would be easy to
wait until the earth's core cools sufficiently (you could work on some of the unsolved pse puzzles to pass the time) and then build yourself a cylindrical house through the center of the earth with one end facing north and one end facing south. Easy peasy, if somewhat lacking in charm and airiness.
Build a house that faces North, South, East and West. Then build two more houses, immediately ajoining the first, on the East and West sides.
The first house now faces North and South, but without any outside walls on its sides, it will not be facing East or West
credit to Strawberry for the idea.
Follow the fashion for environmentally friendly houses.
Build the house through a hill, so that it only has two external walls and the sides are inside the hill. This gives good heat insulation, making it energy-efficient.
I have actually seen a house like this, although I don't have photos.
Space station should fulfill these requirements if it orbits around the equator.
It always faces the North and the South as in northern and southern hemisphere of Earth.
Apparently a compass works in outer space though.