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 This answer satisfied the original conditions but is no longer valid.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.
You build a house all the way around the world at the equator. Then there are only 2 outer walls, facing north and south. If you go east or west inside the house, you will come back to where you started and never encounter an outer wall.
A stretched out house that tapers to points on the east and west would only have two faces, north and south.
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.
If you built a house where
The north facing wall is straight, and the south facing wall is also straight, but the east and west walls curve in semi-circles, that house could be said to face both North and South, but not East or West.
I have an idea
We can build a house (but perhaps it is uninhabitable !!)... in such a way that circular roof points to East and a circular floor points to West and have doors / windows on North and South sides.
That satisfies your requirements perhaps!!
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.