Icosahedron House - A simple geometric structure using commonly available materials.
An icosahedron is a simple geodesic dome that is strong, easy to assemble and minimizes waste. With 8' segments, you can add a sleeping or storage loft. The walls can be covered with fabric like recycled billboard tarp or rigid sheets like plywood.

Solution

FRAME: $50-$100
Drill a hole near both ends of twenty-five 8 foot 2x4's and bolt them to 11 stamped metal plates to create a frame with 7 foot tall sides and 110 square feet of floor space.  Steel corner brackets are available commercially for $60/set.  They are also relatively easy to create by hand.  The structure might work with different materials such as bamboo (ends filled with concrete), rough cut lumber or metal pipe.  For example, conduit domes are often made by flattening and drilling the ends before using 1 bolt.

FIRST FLOOR: $75
A wood floor is a nice upgrade.  Add 5 shorter 2x4's, 10 more bolts and 4-5 sheets of plywood to elevate the structure with rocks or concrete blocks.

SECOND FLOOR: $50-$100
A trampoline mat (Permatron fabric) and rope can make a comfortable sleeping loft.  It's easy to find mats with sewn edges and rings for under $80.  A plywood loft or shelves similar to the first floor is also an option.

WALLS: $0-$50
Recycled billboard tarp is much thicker than heavy duty tarp, waterproof, UV stable and potentially free.  One side is usually painted and the other black or white.  Use at least two layers for more strength and to hide the painted side.  Alternatively, "Shade Cloth" allows air to pass through and protects from sun and insects.  It can be attached using the grommets and the frame bolts.  Each wall can also be covered by a single rigid sheet like plywood though it adds $150 to the cost.  Sashes from used Windows can be found for free from window installers.

DOOR: $25
The door needs to fit into a 7 foot tall equilateral triangle.  Picture a rectangle with the top two corners cut off.  It can be created from additional lumber or a lumber covered with more billboard tarp.

ROOF: $0-$50
The roof has a nice overhang if the 5 roof boards are extended by 1-2 feet.  It can use a skin similar to the wall covering.  You can also cover the entire roof with a single peice of fabric with no holes.  Start with with a hexagon with 8 foot sides.  Then overlap one triangle (60 degrees) to leave 5 equilateral triangles that cover the roof perfectly.  Fasten them at the edges.  Alternatively, 5 sheets of plywood can create a strong base that is covered by tarp or other materials later.

ELECTRICITY: $50-$100
A 5-10 Watt solar panel and a 7-10Ah 12V lead acid battery can supply power for three 5W LED lights that are used 5 hours/day and two cell phones.  (add a cigarette lighter receptacle).  This gives a three day buffer and stays within the float charge of the battery.

It adds to the cost, but a custom triangular solar panel with a transparent backing could also act as a window.  It could also incorporate a small computer fan to provide active ventitation at the peak of the structure.

SOLAR WATER DISTILLER: $50-$100
A large sheet of glass (porch or shower door replacement) angled over a shallow watertight base can be used to evaporate and collect distilled water.  Include an overflow drain so the dirty water never touches the glass.  It takes roughly 8-10 square feet of glass to provide water for a family.  The roof can aid in rainwater collection using a suitable gutter and barrel.

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