Here is the Oxford English Dictionary, 2nd ed, entry edited with the Greek
and pronunciation material omitted:
HEADWORD, PRONUNCIATION, AND ETYMOLOGY
parallelepiped ... Geom. Earlier in Gr. form parallelepipedon .., pl. -a.
Often incorrectly .. parallelo- (whence [another pronunciation]).
[ad. Gr. [lots of Greek!] In late L. (Boethius) paralle<overbar>lepipedus,
F. parall<e acute>l<e acute>pip<e grave>de (1570 in Hatz.-Darm.), often
parall<eacute>lipip<egrave>de.]
DEFINITIONS
A solid figure contained by six parallelograms, of which every two opposite
ones are parallel; a prism whose base is a parallelogram.
QUOTATIONS
1570 Billingsley Euclid xi. xxxi. 342 Parallelipipedons consisting vpon
equall bases, and being vnder one and the selfe same altitude, are equall
the one to the other.
1666 Boyle Orig. Formes & Qual. (1667) 42 Though Spheres and
Parallelopipedons differ but in shape.
1667 Collins in Rigaud Corr. Sci. Men (1841) II. 479 By producing the
planes of the parallelepipedons, so that their sides shall cut off (viz.
each parallelepiped twelve) second segments in the whole equal.
1791 Hamilton Berthollet<cq>s Dyeing I. i. iii. vii. 275 White crystals in
flat parallelipipedons.
1857 Birch Anc. Pottery (1858) I. 12 These bricks are all parallelopipeda,
of Nile-mud or clay of a dark loamy colour, held together by chopped straw.
<gk><beta></gk>.1663 Charleton Chor. Gigant. 21 Resembling Parallelipipeds,
rather than Cylinders.
1667 Parallelepiped [see <gk><alpha></gk>].
1744 Phil. Trans. XLIII. 29 This Parallelopipede Figure with oblique Angles
is common to many Stones.
1812<min>16 Playfair Nat. Phil. (1819) I. 183 If a rectangular
parallelepiped float in a fluid.
1868 Grove Contrib. Sc. in Corr. Phys. Forces (1874) 449 A slab of stone of
a parallelopiped form.
rectangular parallelepipeds.
RELATED FORMS
Hence
parallelepipedal, parallele<ph>"</ph>pipedonal (irreg.),
parallele<ph>"</ph>pipedous adjs., having the form of a parallelepiped.
MORE QUOTATIONS FOR THESE
1754 New & Compl. Dict. Arts & Sci. II. 1394/1 The capacities of all sorts
of vessels.., as cubical, parallelopipedal, cylindrical,..&c. are computed.
SNIP
1890 Century Dict., Parallelepipedonal.
1950 L. R. Underwood Rolling of Metals I. iv. 83 If a rectangular network
of lines on the bar before rolling is still rectangular after rolling, then
the total deformation may be regarded as parallelopipedal.
1974 Chem. Physics VI. 2/2 The term <oq>unit cell<cq> will be retained
here..to mean the parallelepipedal cell (whether primitive or multiple)
used by crystallographers.
MY NOTES
There is an alpha before the Billingsley entry, meaning 'before' or 'not
later than'.
There is a beta before the 1663 Charleton entry, meaning?
Billingsley is indeed the first printed usage, with the spelling shown, and
thereafter it is used by mathematicians with various spellings; see 1666
Boyle, 1667 Collins in Rigaud .., 1744 Phil. Trans. XLIII. 29 This
Parallelopipede Figure ... The last usage in 1974 is in chemistry.
ANOTHER DICTIONARY DEFINITION is very brief:
parallelopiped, etc., erroneous spelling of parallelepiped, etc [!!]
I haven't checked other possible variant forms, but I suspect they don't
exist or are like this one. (Such a check might be easier with paper
edition.)
'Correct' spelling didn't start until the 19th century. (Correct?) For
example, we have only 3 signatures by Shakespeare, all spelt differently.
(Correct?)
Don't forget that the OED is a historical English dictionary, so less
emphasis on US usage.
David Fowler