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Apart from the general structure (6 layer cortex, same areas, etc.) does every brain have the exact same number and arrangement of sulci, gyri, etc? Do these elements have the same shape?

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No, not at all--or not necessarily; different sulci & gyri may be different shapes--this is one of the reasons why individual brains are transformed or normalized into standard space in group analysis of MRI data (see here for a good basic explanation of how & why this is done). In some cases canonical landmarks may be missing entirely--famously, an autopsy showed Albert Einstein to have quite anomalous anatomy in the area of the frontal operculum or Sylvian fissure.

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