Below, list is a representative sample of my list, which contains lists of integers. I would like to be able to input:

list = {{1, 2, 3}, {3, 2, 1}, {2, 1, 3}};
f[list]

and obtain the output:

{{1, 2, 3}, {2, 1, 3}}

In other words, {3, 2, 1} is considered to be the same as {1, 2, 3}, since in reverse it is exactly {1, 2, 3}. However, {2, 1, 3} is not considered to be the same as either {1, 2, 3} or {3, 2, 1}, because it does not match these lists in forward or in reverse.

What function f can I use to accomplish this?

I tried this:

DeleteDuplicates[list, MemberQ[list, #] || MemberQ[Reverse /@ list, #] &]

but it does not work, although I'm not sure why.

Below, list is a representative sample of my list, which contains lists of integers. I would like to be able to input:

list = {{1, 2, 3}, {3, 2, 1}, {2, 1, 3}};
f[list]

and obtain the output:

{{1, 2, 3}, {2, 1, 3}}

In other words, {3, 2, 1} is considered to be the same as {1, 2, 3}, since in reverse it is exactly {1, 2, 3}. However, {2, 1, 3} is not considered to be the same as either {1, 2, 3} or {3, 2, 1}, because it does not match these lists in forward or in reverse.

What function f can I use to accomplish this?

I tried this:

DeleteDuplicates[list, MemberQ[list, #] || MemberQ[Reverse /@ list, #] &]

but it does not work, although I'm not sure why.

ADDENDUM

Now suppose I want to input:

list = {{1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {1, 2, 3}};

and obtain:

list = {{1, 2, 3}, {2, 1, 3}};

where the "second" {1, 2, 3} is removed as a "normal" duplicate. How can I do this? I could do:

DeleteDuplicates[DeleteDuplicates[list, (#1 == Reverse[#2] &)]]

but is there an easier way?