Symmetries of the alphabet.The letters of the alphabet exhibit five varieties of symmetry (or non-symmetry):
A M T U V W Y have left-right (vertical) symmetry (.272) v B C D E K have up-down (horizontal) symmetry (.218) h N S Z have 180[degrees] (rotational) symmetry (.137) r H I O X have all three symmetries (.205) a F G J L P Q R have no symmetry (,168) n
In running text, thee various symmetries appear with the indicated probabilities; for example, left-right symmetry occurs twice as often as rotational symmetry,
These appear to be all the possible theoretical symmetries. In particular, it is impossible to create a "letter" with two but not three symmetries, i.e., with left-right and rotational (but not up-down), with up-down and rotational (but not left-right), or with left-right and up-down (but not rotational) symmetry.
Can one locate a set of 120 five-letter heterograms which contain one letter with each kind of symmetry, arranged in all possible symmetry orders? Using only words in boldface from Webster's Second or Third (plus inferred forms such as past tenses and plurals), it appears to be impossible. One difficulty appears to be that vowels are contained in only 3 of the 5 symmetries. If one allows OED words or placenames, however, then a full collection is likely possible.
The collection below is restricted to Websterian words. Each possible ordering is identified by lower-case letters vhran. Although only a couple of examples are typically shown, a few orders are especially fecund:
navhr GIVEN LIVEN RIVEN GIVES LIVES FIVES RIVES LIMES RIMES RITES LOVES LOADS ROADS GOALS hnavr CLOYS CLOTS BLOTS BLOWS BROWS CROWS BLOWN BROWN CROWN CLOWN BRIMS DROWN rvanh SMILE SMIRK SHORE SWORD STILE SWIPE STOLE STOPE STORE STORK
ahvnr HEAPS HEALS
arhnv INEPT INERT
arvnh INURE To result; to take effect; to be of use, benefit, or advantage to an individual.
For example, when a will makes the provision that all Personal Property is to inure to the benefit of a certain individual, such an individual is given the right to receive all the personal
avrhn OWNER HAZEL
hanvr KORAN BOGUS
harnv CONGA DINGY
havnr BOARS CHAPS
havrn BHANG bhang also bang
A preparation from the leaves and seed capsules of the cannabis plant, smoked, chewed, eaten, or infused and drunk to obtain mild euphoria.
hnarv BRINY KRONA
hnavr BROWN CLOTS
hnvar DRAIN BLITZ
hnvra BRUSH CLASH
hrvan ESTOP estop v. to halt, bar or prevent. (See: estoppel)
hvanr BAIRN bairn
[Middle English barn, from Old English bearn; see bher-1 in Indo-European roots. CAIRN
hvnar BARON CAPON capon
castrated male fowl, larger than broiler, weighing up to 7 lb; produced either by administration of estrogenic substances or by surgical excision of the testicles.
nahvr FOCUS LOCUS
narhv FONDU RISKY
narvh GONAD gonad /go·nad/ (go´nad) a gamete-producing gland; an ovary or testis.gonad´algonad´ial
indifferent gonad the sexually undifferentiated gonad of the early embryo.
navhr GIVEN LOVES
navrh FOUND PHASE
nharv FEINT PEONY
nhrva PESTO LENTO
nvrah PANIC RUNIC (jargon) runic - Obscure, consisting of runes.
VMS fans sometimes refer to Unix as "RUnix". Unix fans return the compliment by expanding VMS to "Very Messy Syntax" or "Vachement Mauvais Systeme" (French; literally "Cowlike Bad System", idiomatically "Bitchy Bad System").
nvrha LYNCH JUNCO junco or snowbird, small seed-eating bird of North America closely related to the sparrows. Juncos have white underparts and gray (sometimes also brown) backs. They travel in flocks.
rahvn SHEAF SIBYL
ranhv SHREW SILKY
ranvh SHRUB SOLVE
ravhn NITER niter or nitre: see potassium nitrate. SOWER
ravnh SHAPE SHARK
rhavn SCOWL SKIMP
rhnav SCRIM SEPIA
rhnva SERMO SEPTI
rnahv SPICY SPIKY
rnavh SLIME SPITE
rnvah SQUIB SQUID
rvahn STOEP stoep
(in South Africa) a verandah [Afrikaans]
Noun 1. stoep - small porch or set of steps at the front entrance of a house
rvanh SMILE SMIRK
vanhr WORDS MILKS
varnh AISLE TINGE
vhanr ACORN ADORN
vhnar AEGIS MELON
vhnra VERSO WELSH
vnahr ALIEN TRIES
vnarh ALONE ARISE
vranh ANILE an·ile
1. Of or like an old woman.
Finally, a challenge to computer programmers: can the alphabet be partitioned into five groups so that all 120 permutations can in fact be found among Websterian heteronyms?
A. ROSS ECKLER
Albert Ross Eckler (May 22, 1901 - March 14, 1991) served as deputy director of the United States Census Bureau from 1949 to 1965, and its director from 1965 until 1969.
Morristown, New Jersey Morristown is a town in Morris County, New Jersey, United States. As of the United States 2000 Census, the town population was 18,544. Its estimated population in 2004 was 18,842. It is the county seat of Morris CountyGR6.