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Who says they are? For instance, a circle inversion might map a circle into a line.

Conformality is a strictly local property - it just says that if two curves crosses each other with some angle between them at the intersection point, the angle will be same on the map produced by a conformal transformation.

i am referin to the mandelbox definition here
https://sites.google.com/site/mandelbox/what-is-a-mandelbox

where he states that by liouvilles therem all such are shape preserving....
http://en.wikipedia.org/wiki/Liouville%27s_theorem_%28conformal_mappings%29

I think Liouville's theorem states what the possible conformal transformations in 3D are. I don't see see any mentioning of shape. Indeed, Wikipedia describes conformal transformations as angle-preserving, and notes that "Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size.". And as kram noted only local (but not global) undistortion is ensured.

I personally don't think it is correct to talk about inversions as a shape preserving transformation, for instance, it is not included on this list:
http://mathcentral.uregina.ca/QQ/database/QQ.09.98/mcandrew1.html
and I couldn't find any examples, but I might be wrong. At least it would be clearer to say it is locally shape preserving,

For a good illustration of angle-preservation, see this list of conformal map projections:
http://www.progonos.com/furuti/MapProj/Dither/ProjConf/projConf.html

They all conserve the angles (look at the right angles between the longitude and lattitude lines), but the shapes are quite different.