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The plural of the noun appendix in its academic sense of a non-essential addition to a piece of writing is appendices (pronounced 'er-PEN-dis-eaze'). This should always be true in academic English, although the form appendixes is also to be found in less formal writing and in medical circles, where it denotes what is more technically named the vermiform appendix.

Appendix was originally a Latin word. Most nouns in Latin that end in -ix form the plural in -ices. So when you say appendices, you are showing that you are a real academic - you [are pretending to] talk Latin. (See -es in Latin for a brief explanation.)

Beware: the use of the word appendix as a verb ('to appendix'), as in 'he appendixed his data to his report', meaning 'he gave the data as [or in] an appendix to his report', is frowned on in academic British English. It is more elegant - and grammatically accurate - to
use append as the verb: 'he appended his data to the report'. 
Don't confuse appendix with appendage. (Both are derived from the Latin appendĕre , formed from ad- 'to' and pendēre 'to hang' (intransitive), which also gives us the verb append.) The noun 'an appendage' is nowadays reserved for an item subordinate to a more important item, in itself more or less unnecessary, or irrelevant to the writer's current purpose.