Closely related to palindromes, symmetrical words are words that have an axis of symmetry, or point of rotational symmetry. Needless to say, it is relevant whether the word is written in upper or lower case.
Some long words with horizontal symmetry are: BEDECKED, BOOHOOED, CHECKBOOK, CODEBOOK, COOKBOOK, DECIDED, DIOXIDE, DOBCHICK, EXCEEDED, HOODOOED, and KEBOBBED. The longest such word, with ten letters, is OKEECHOBEE.
The longest words with vertical symmetry are OTTO, MAAM, and TOOT. Others include MOM, WOW, AHA, AHA, AIA, AMA, AVA, AWA, HAH, HOH, HUH, MAM, MIM, MUM, OHO, OXO, TAT, TIT, TOT, TUT, UTU, VAV, and WAW!
When written in upper case, the word BID has horizontal symmetry, but when written in lower case it has vertical symmetry – bid!
SWIMS is probably the longest word with 180-degree rotational symmetry. All of the letters in the words SOONISH (7 letters) and ONIONS (6 letters) independently have 180-degree rotational symmetry.