If you have only one tree, the most obvious choice of house design is one that surrounds the tree trunk. The floor will be held up by supports that radiate outward from the trunk. These 'spokes' can be supported using either knee braces underneath (in compression) or from cables or braces above (in tension). Tension braces are not covered by this article, but work in a similar manner to upside down knee braces with the treehouse suspended underneath.
A steel cable may be secured to the end of each spoke, reaching to a point higher up the tree where it is fastened to an eyebolt. This cable can get in the way of the superstructure of the house, but alterations can alleviate the problem. Each spoke can be lengthened and the cables sent up at a steeper angle so they clear the walls and roof. A scale drawing may be necessary to calculate the angles and lengths you need. See the cables page.
Building around a tree lends itself to a circular structure, but be aware that creating any kind of curve in wood is much more time consuming than if everything runs together at right angles. Hexagonal and octagonal houses are also beautiful but can involve awkward geometry that can slow up the building process.
You may consider using posts in addition to the tree to allow greater possibilities. Although it will not strictly be a treehouse, you will be able to use more rectangular floor spaces or add a large deck to your existing design. See the no trees page.