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I know that for a carbon to be chiral four different groups should be attached to that particular carbon. But, what about in the case of cyclic compounds? What's the method to check chirality if the carbon is not $\mathrm{sp}^3$ hybridized and only three, or two groups are attached to it (through double or triple bonds)?

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If an atom is part of a double or a triple bond it is never a stereogenic center because then this atom and the atoms bound to it form something planar, so that you can always find a symmetry plane. But an atom that is part of a double bond can be prochiral, if it can be converted from to a stereogenic center in a single step.

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  • $\begingroup$ Allenes can be chiral $\endgroup$ – K_P Oct 29 '14 at 0:45
  • $\begingroup$ @K_P That's true, good point. But still their ($\ce{sp^{2}}$ carbon) atoms are no stereogenic centers. $\endgroup$ – Philipp Oct 29 '14 at 9:27
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    $\begingroup$ But if the question is about chirality, a molecule having stereogenic centres is not a sufficient (eg. meso compounds) nor a necessary (as in the case of allenes or eg atropisomers) condition for it to be chiral. $\endgroup$ – K_P Oct 29 '14 at 19:46
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    $\begingroup$ @K_P He asked about chiral carbon atoms and since I had been quite busy at the time I only provided an answer within that scope. If you want to add an answer including axial chirality you are welcome. I'll happily upvote it. $\endgroup$ – Philipp Oct 29 '14 at 20:30
  • $\begingroup$ I don't think a new answer is needed, you already provided a very good one and one that OP was happy with. I just added my comment as additional information. $\endgroup$ – K_P Oct 29 '14 at 20:42

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