What is the molecular shape of AX6E?

Question

What is the molecular shape of AX6E and give an example.

with A being the central atom

X being the bonded atom

E being the number of lone pairs

Answer 1

AX6E tells us that attached to the central atom are six atoms, so there six bonding pairs and a lone pair, for a total of seven electron pairs.  That is past the fairly simple octahedral arrangement and into territory that we normally don't teach to first year high school and college students.

That geometry would be pentagonal pyramidal, and an example is  XeF6

Answer 2

Whoever asked you the question needs to rethink why you're learning about bonding theories.   We don't teach you these things to make blind predictions disjointed from any experimental reality - bonding theories are used to rationalize structural data after the fact, to explain what actually happens.  The only possible answer answer to your question requires picking a specific compound, looking up it's actual structure, and then seeing if you can use VSEPR to rationalize it.

So what actually happens in an AX6E?

I don't know where pisgahchemist is getting his data, but XeF6, although it is an AX6E complex, is NOT a pentagonal pyramid.  As far as I know, its structure has not yet been definitively experimentally determined, but among the leading candidates are c3v and C2v distorted octahedra and an undistorted octahedron -- a C5v pent pyramid is NOT a possible structure.  

See Journal of Molecular Structure: THEOCHEM, 2001, 540, 29-33 and J Chem Phys 1975 63 3849-56.

Cacluations in J. Am. Chem. Soc. 1996, 118, 11939-11950 show that other isoelectronic ions have similar problems.  [IF6]– [TeF6]2– [SeF6]2–, they sit on a knife's edge of stability between c3v and Oh structures.  Again, no C5v pent pyramid.  Other AX6E ions are mostly Undistorted octahedron, where the LP is NOT sterochemically active.

A salient quote from the latter paper:

"This series of compounds is also a challenge to the qualitative

interpretation of molecular structure. We have shown that of

the various model approaches discussed in section 2 of this paper

each has some merit. However, all of them fail to explain why

XeF6 is a distorted octahedron while most of the ions valence isoelectronic with it are not. In particular, XeF6 is not a

manifestation of the VSEPR model. ... Reality is different. This

is a warning to overestimate the reliability of models based on

orbital interactions alone."

What's the molecular shape of AX6E?  Hard to say.  Often, undistorted octahedron, but in many cases it's a slightly distorted octahedron with either C3v or C2v symmetry.  Can you use VSEPR to rationalize those structures?  No, not a chance.