Last revision: Dec. 24, 2017
On this page, “the five vowels” refers to a, e, i, o, u, and “the six vowels” refers to those letters plus the letter y.
Words consisting entirely of vowels include A, AA (a type of lava), AI (the three-toed sloth in Chambers and a Biblical place name and a Russian river), AIEEE (an interjection in the OED), AIOUEA (a genus of the laurel family (Lauracea) [Charles Turner], EUOI (cry of Bacchic frenzy), EUOUAE, I, IAO, IO, (an interjection in Chambers; one of the moons of Jupiter), IOUEA (a genus of Cretaceous fossil sponges), O, OII, OO ("wool" in Scottish), UOIAUAI (a language in Par´ State, Brazil) [Dmitri Borgmann, in Charles Bombaugh's Oddities and Curiosities of Words and Literature).
The scientific name of the roseate spoonbill is AJAIA AJAIA (or AJAIA AJAJA); however, the J's would have been I's in the original Latin spelling, so that the words would consist entirely of vowels also.
Some all-vowel Hawaiian names for birds which are used in English are AO - Puffinus puffinus (Manx shearwater), UAU - Pterodroma phaeopygia (Dark-rumped Shearwater), OEOE - Oceanodroma castro (Harcourt's Storm-petrel), IO - Buteo solitarius (Hawaiian Hawk), OOAA - Moho bracatus, OU - Psittirostra psittacea.
All-vowel words in the OSPD3 are AA, AE, AI, EAU, OE.
Allowing proper nouns, some words consisting only of vowels include AIEA (a city in Hawaii), EIAO (one of the Marquesas Islands), EA (a town in the Basque section of Spain), AEAEA (the legendary home of Circe in the Tyrrhenian Sea), AAUAUA (a river in Brasil), II (a place in Finland 40 km north of Oulu), and OUEOI (an ancient Tuscan city in Etruria). IO is the only name on any hurricane name list which consists entirely of vowels. It is on the Central Pacific hurricane name list [Brett Brunner, Juozas Rimas, Stuart Kidd, Pertti Malo]. Dmitri Borgmann gives OEAEI (the name of the wife of Ra-amen, the spondist of Pthah) [An Archaic Dictionary, From the Egyptian, Assyrian, and Etruscan Monuments and Papyri, by William R. Cooper, London, 1876]. OUADI EL AOUAOUIYE is a location in Syria, AOUEOUA in Mauritania, and AOUEOUE in Togo [Rex Gooch].
Allowing Y as a vowel, some words consisting only of vowels include AYE, AYU, EYE, IYO, EYEY, and YAYA (although I am not sure which of these Y's are vowels!).
The Hawaiian word HOOIAIOIA (meaning "certified") has eight consecutive vowels and is listed in the 1976 Guinness Book of World Records [Charles Turner].
Allowing proper nouns, IJOUAOUOUENE, a mountain in Morocco, has 8 consecutive vowels as rendered by the French [Guinness]. Also with 8 consecutive vowels are the Bled El HAOUAOUIA area and OUAOUIOUST hill (both in Morocco), AGUINAOUIAOUI in Mali, and ISSOUOUAOUAR in Niger [Susan Thorpe]. In Estonian, ÕUEAIAÄÄR means "edge of a fence surrounding a yard" [Juozas Rimas, Ahto Truu].
Trevelyana kouaouae, a species of sea slug, has 7 vowels in a row [Charles Turner]. A place name with 7 vowels in a row is OUAOUIATON, which appears on a French map of the central part of North America printed in 1693 The word was later shortened to OUAOUIA, and was applied to the Indian tribe subsequently called Iowa. [The Book of Names, J. N. Hook.] Other place names with 7 vowels in a row include AOUEOUA, (Mauritania), AOUEOUE, Togo, BOUAAOUAM (Algeria), TIOUOOUORT (Mali), and ES ZOUAOUIINE and TAZOUOUOUARHT (Morocco) [Susan Thorpe, Rex Gooch].
In Dutch, KOEIEUIER (the udder of a cow) and PAPEGAAIEËIEREN (parrot eggs) have seven consecutive vowels, although they are no longer valid spellings, having been replaced by KOEIENUIER and PAPEGAAIENEIEREN [Joost Gestel, Tom Vernooij, John Slegers].
Words with six consecutive vowels include EUOUAE, which W2 defines as “A word formed from the vowels of seculorum amen, ending the Gloria Patri,” AIOUEA (a genus of plants of the laurel family), DIOOEAE (a tribe of cycads), and Corydalis aeaeae (an herb). [Charles Turner].
The ZOUAOUA are a Kabyli tribe living in Algeria and Morocco. UAIEUE (variants: UAIUAI, WAIWAI or OUAYEONE) is a language of Brazil indians. AAUAUA is a river in Brasil. These words have 6 consecutive vowels [Juozas Rimas]. Also with six consecutive vowels is INOEIOIO in Mozambique [Susan Thorpe].
The Dutch word ZAAIUIEN (onions for seeding) has 6 consecutive vowels, still valid in the new spelling since 1995, although this is not found in the Van Dale dictionary [Oscar van Vlijmen].
Words with five consecutive vowels include QUEUEING, the interjection AIEEE, which is in the OED, and COOEEING. (COOEE or COOEY, a peculiar cry of the Australian aborigine, is in W1, W2, and W3. The word is also a verb and both W1 and W2 show the forms COOEEING and COOEEYING.) The OED2 has COUUIENALES, which is a variant of quienals, which comes from quiennal, meaning "dispensation or indulgence for five years." Other such words are MIEAOU (OED) and MIAOUED and MIAOUING (what a cat does; OSPD and Webster's Collegiate Dictionary, 5th edition), ROUSSEAUIAN (relating to the French philosopher Jean-Jacques Rousseau), ZAOUIA (an alternate spelling of zawiya according to the OED2 - Jeremy Marshall), JUSSIEUEAN ("pertaining to the natural system of botanical classification devised by Bernard de Jussieu and his nephew Antoine Laurent de Jussie" [W3]) and ZOOEAE (larvae of crabs and relatives [Chris Cole]) or ZOAEAE [OED]. The Kaula (Pteralyxia kauaiensis) and the Holei (Ochrosia kilaueaensis) are endangered Hawaiian plants, and the Formosan Sika (Cervus nippon taiouanus) is an endangered Taiwanese deer. MIOEUOTICUS is a primate genus. PIVETEAUIA is an extinct genus of prehistoric coelacanth fish. PANOOUEI is the name of a village in Egypt mentioned in a papyrus written in Greek in the 4th century A. D., as deciphered by Kyle Helms of the University of Cincinnati, according to news reports in 2014. Cyclostremiscus beauii is a Marine snail from Florida and Chicoreus beauii is Beau’s murex sea snail [Charles Turner, Philip Bennett].
The entomologist A. A. Girault named a group of tiny wasps for writers, scientists, statesmen, and philosophers (Shakespearia, Beethovena, Goetheana, Marxella, etc.). He named a wasp genus THOREAUIA for Henry David Thoreau. This word has five consecutive vowels [Charles Turner].
Some words with four consecutive vowels follow (although in some of these words the Y may not actually be a vowel): aqueous, Archaeoastronomy, Archaeoindris fontoynonti (an extinct species of lemur), Aysheaia ( fossil onychophoran), ballyhooey, bayou, biyearly, buoyance, buoyancy, buoyant, buoyed, buoying, clayey, dequeue, dequeuing, employee, enqueue, Epopoeia, eyeing, flooey, Gnaoua (a Moroccan ethnic minority group and part of the name of the Gnaoua & World Music Festival which is held annually in Essaouira, Morocco, which also has four consecutive vowels), gooey, guaiacum, Hawaiian, hooey, joyous, kayoed, kayoing, layout, layouts, Lithophane leeae (a moth), maieutic, obloquious, obsequious, onomatopoeia, palaeoanthropic, palaeoanthropology, Paraguayan, payee, pharmacopoeia, prosopopoeia, Quaoar (a term in the creation mythology of the Tongva people and a Kuiper Belt object discovered in 2002), quayage, queue, queuine (a chemical name), radioautograph, reliquiae, royaux, Rubaiyat, Sequoia, subaqueous, terraqueous, Uruguayan, Vegavis iaai (Late Cretaceous bird from Antarctica), voodooienne, voyeur, Yaounde [Nelson H. F. Beebe, Charles Turner, Paul Wright].
These words begin with four consecutive vowels: UEUETEOTL (an Aztec god), EUAECHME (a character in Greek mythology), and AEAETES (a character in Greek mythology) [Charles Turner].
Seven-letter words with the five vowels are SEQUOIA, EULOGIA, EUNOIA (alertness of mind and will), MIAOUED, ADOULIE, EUCOSIA, EUNOMIA, EUTOPIA, MOINEAU, DOULEIA (an alternate spelling of DULIA which appears in W2), and EUODIAS (a name in Philippians 4:2). Allowing scientific names in biology, IOUEA is a genus of Cretaceous fossil sponges. BOIEAU is a town in Belgium. POAEUI Passage is in Papua New Guinea. Olaudah EQUIANO was the most prominent Black figure involved with the British abolition movement, through promotion of his best-selling autobiography. [Philip Bennett, Susan Thorpe, Stuart Kidd, Rex Gooch]
Eight-letter words with the five vowels are AEGOLIUS (a genus of owls), AEQUORIN, AEROBIUM, AGOUTIES, AUREOLIN, CAJUEIRO (a municipality in Brazil), DIALOGUE, EDACIOUS, EQUATION, EULOGIAS, EUPHONIA, EUPHORIA, EUSOCIAL, EXONUMIA, FONUALEI (a volcanic island in the kingdom of Tonga), GAULIOSE, GEROUSIA, JALOUSIE, LEXIAGUO (place name in China), OECIACUS (a genus of bugs), OMEISAUR (a genus of sauropod dinosaur), OUTRAISE, SAUTOIRE, SEQUOIAS, and THIOUREA [Philip Bennett, Charles Turner].
Eight-letter words containing the six vowels are EUMYOBIA, EURYOMIA, EURYOPIA, EYDOUXIA, IALOUSYE, and JOYEUXIA [Stuart Kidd, Charles Turner].
Nine-letter words with the five vowels occurring once are ANDOUILLE, ARMOURIES, AUTOPSIES, AUTOMERIS (a genus of moths), BEHAVIOUR, CETIOSAUR, COATLIQUE (the Aztec goddess who gave birth to the moon, stars, and Huitzilopochtli, the god of the sun and war), DEIPAROUS, EDUCATION, FAVOURITE, LOUISELLA, NAUSCOPIE, NEFARIOUS, ODALISQUE, OPITULATE, OSSUARIES, PEIROSAUR, PNEUMONIA, VEXATIOUS, VINACEOUS, and VOLUTIDAE [Charles Turner].
Nine-letter words containing the six vowels are OXYURIDAE (pinworms), OXYGEUSIA (abnormal sensitivity to taste), OXYURINAE (a sub-family of ducks), and SEYMOURIA (genus of fossil amphibian). [Chris Cole, K. K. S. Bisht, Charles Turner].
Ten-letter words with the five vowels are AUTHORIZED, BIVOUACKED, COAHUILTEC (an Indian people of northeastern Mexico and Texas), DISCOURAGE, ELUCTATION, EXHUMATION, GREGARIOUS, KERATINOUS, MAIOCERCUS (a fossil arachnid), MENDACIOUS, MORTUARIES, MOUSTERIAN (the style of tool made by Neandertals), NEUTRALINO, NUCLEATION, OUTPATIENT, PHONEUTRIA (the world’s most venomous spider, Greek for “murderess”), PLESIOSAUR, PRAETORIUM, PRECAUTION, QUATERNION, PRECARIOUS, PREDATIOUS, RHEUMATOID, SEABORGIUM, SEQUACIOUS, SIALOQUENT, TAMBOURINE, TOURMALINE, TROUVAILLE, UROGENITAL, and VAPOURISED (British spelling) [Charles Turner].
Ten-letter words containing the six vowels are ANEUPLOIDY, AUDIOMETRY, AUREOMYCIN, BUOYANCIES, AUTOTYPIES, COEQUALITY, EUKARYOTIC, OXYURIASES, and SEYMOURINA (a new Paleozoic fossil plant) [Philip Bennett, Stuart Kidd, Charles Turner].
Eleven-letter words containing the five vowels are CLAVIGEROUS, EPIZOANTHUS (a genus of zoanthidean anemones), FORMULARIES, GLUCOSAMINE, GLUCOSIDASE, GLUTATHIONE, (an antioxidant), GOURMANDIZE, HUITLACOCHE (a fungus of the mushroom family that grows on corn), IMPORTUNATE, MUSTACHIOED, PANDEMONIUM, PHOBAETICUS (a stick insect and at 22.3 inches, the longest insect in the world), SPECULATION, and TSUKIYOTAKE (a toxic, bioluminescent Japansese mushroom).
Eleven-letter words containing the six vowels and none repeated are NEFARIOUSLY, PALEOXYURIS, VEXATIOUSLY, TENACIOUSLY, BOUIACHELYS (extinct marine turtle), EQUIVOCALLY, APODYTERIUM (in ancient Rome, the changing room before you entered the baths), which was used in the 2009 Scripps Spelling Bee) [Charles Turner].
Twelve-letter words with the five vowels are BUITRERAPTOR (a genus of dinosaur), EUHAPLORCHIS (a genus of parasite), MAGNILOQUENT, PAMBDELURION (a blind nektonic organism from Cambrian Greenland), PUTREFACTION, SPACIOUSNESS, STERNUTATION, STUPEFACTION, VULCANOLEPIS (a genus of barnacle), and PRESTANTIOUS (from the Latin praestantia, meaning “excellence”; the OED shows only one use of the word, in 1630). [Charles Turner]
STYGIOMEDUSA (a giant deep-sea jellyfish), PRASEODYMIUM (element 59), and EUPHORICALLY are 12-letter word with the six vowels [Charles Turner].
The 12-letter obsolete word TWYNDYLLYNGS contains none of the usual vowels, although y is a vowel in this word. [Charles Turner]
RHABDOPLEURID, FAULCONBRIDGE (a town in Australia), BURNETIAMORPH, HAUFFIOPTERYX (a genus of ichthyosaur), and AMPLITUHEDRON (a geometric structure discovered in 2013) are 13-letter words with the five vowels. [Charles Turner]
MYCOBACTERIUM, EUCRYPTODIRAN (turtles and tortoises which are able to retract their heads completely into their shells), HYRACOTHERIUM, PSITTACEOUSLY, and MONUMENTALITY are 13-letter words containing the six vowels with none repeated. Another such word is Paucidentomys vermidax, a shrew-like animal announced in 2012 [Charles Turner].
GLAUCONYCTERIS (a genus of bat) and THYSANOTEUTHIS are 14-letter words containing the six vowels [Charles Turner].
SACRILEGIOUSLY is a 14-letter words with the vowels in alphabetical order, although i repeats. [Charles Turner]
Fifteen-letter words with the five vowels and none repeating are COUNTERCHANGING, COUNTERCHARGING, COUNTERMARCHING, COUNTERSHADINGS, NONINSTRUMENTAL, PITHECANTHROPUS, SCHISTOCEPHALUS, STREPTOBACILLUS, ULTRAMODERNISTS, and UNSPORTSMANLIKE. [Charles Turner, Paul Wright].
PHYCODNAVIRUSES is a 15-letter word with the 6 vowels and none repeated [Charles Turner].
EURYGNATHOHIPPUS (a genus of fossil horse) is a 16-letter word with the 6 vowels but one repeated [Charles Turner].
Pierre Abbat believes that FRACEDINOUSLY is the longest word that has all six vowels in order and no repeated letters.
The longest word with the five vowels in alphabetical order is PHRAGELLIORHYNCHUS (a protozoan) [Susan Thorpe].
The shortest with the six vowels in alphabetical order is AERIOUSLY (in the OED, meaning “airily”). A slightly longer such word is HAREIOUSLY (cruelly), which the OED2 shows in a single citation from a 15th-century manuscript [Susan Thorpe].
The longest word containing all six vowels, with each vowel occurring only once, is ANTISTREPHORRHYNCHUS (an extinct crustacean) [Susan Thorpe]. Other long words are HYDROMETALLURGISTS and NONUNDERSTANDINGLY [Stuart Kidd]. The longest words containing the six vowels in alphabetical order, each occurring only once, are ABSTENTIOUSLY and MARVEILLOUSLY (variant of marvellously) [Susan Thorpe].
The longest words containing the five vowels in alphabetical order are SUPERCALIFRAGILISTICEXPIALIDOCIOUS (34) and PANCREATICODUODENOSTOMIES (25) [Stuart Kidd].
According to Philip Bennett, the longest words containing the six vowels in alphabetical order are PANCREATICODUODENOSTOMY and PANCREATICODUODENECTOMY (in the Merriam-Webster Medical Dictionary).
The Czech word MATEŘÍDOUŠKY (“thyme plants”) has all six vowels in alphabetical order [Jan Pulkrábek]. The Latin word MALEFICORUM (genitive masculine plural of maleficus) has the five vowels in alphabetical order [Charles Turner].
Each of the five vowels occurs in both words of the title AMOENITATUM EXOTICARUM, a book written and illustrated by Engelbert Kaempfer and published in 1690 [Charles Turner].
Pierre Abbat says ACEITOU (Portuguese for past tense of to accept) and ALEIJOU (Portuguese for past tense of paralyze) are the shortest words he knows in any language written in the Roman alphabet which have all five vowels in order.
A species of louse, Haemodipsus lyriocephalus, has all the vowels once in each name [Stuart Kidd].
ULTRAREVOLUTIONARIES has each vowel exactly twice. The shortest such word is CUBOIDEONAVICULARE (Ligamentum cuboideonaviculare), and the longest, USSOLZEWIECHINOGAMMARUS (a small crustacean) [Susan Thorpe]. PSEUDOPSEUDOHYPOPARATHYROIDISM (which is in OED2) has each vowel at least twice.
OUENOUAOU (a stream in the Philippines) has vowels for 8 of its 9 letters and may be the longest place name with one consonant. PUNAAUIA (a village in Tahiti) has vowels for 6 of its 8 letters [Juozas Rimas]. OUABAIO (an African tree) has vowels for 6 of its 7 letters [Stuart Kidd]. OGOOUE (an African river) has vowels for 5 of its 6 letters.
Words with the five vowels in reverse alphabetical order are: DIPLUROIDEA (a superfamily of funnel-web tarantulas), DUOLITERAL, JULOIDEA, MOLLUSCOIDEA, MUROIDEA (the mice-like rodent family), LEEUWENHOEKIELLA (a marine bacterium), MUSCOIDEA (the family of two-winged flies), PAGUROIDEA (the superfamily to which hermit crabs belong), PULMONIFERA, PRUNOIDEA (a suborder of radiolarian protozoa), PUNCTOSCHMIDTELLA (a crustacean), RUDOIERA, SUBCONTINENTAL, SUBHYOIDEAN (beneath the hyoid bone), SUBPOPLITEAL, SUBVOICEBAND, SUOIDEA (the group to which pigs belong), QUODLIBETAL (of an issue that is presented for formal disputation), QUODLIBETARY (a quodlibetical argument), TUTOIERA, UNCOMPLIMENTARY, UNCONSIDERABLY, UNCONTINENTAL, UNCONVINCEABLY, UNNOTICEABLY, UNOBLITERABLY, UNOCCIDENTAL, UNORIENTAL, UNPOLICEMANLY, and UNPROPRIETARY [Philip C. Bennett, Charles Turner, Stuart Kidd, Paul Browning, Susan Thorpe, Dmitri Borgmann.
PACHYCEPHALOSAUROIDEA (a superfamily of ornithischian dinosaurs), DASYUROIDEA (Superfamily of marsupials), and OXYUROIDEA (Order of nematode worms) contain the six vowels in reverse alphabetical order [Charles Turner].
CWM (a glacial hollow on a hillside) has the rare W as a vowel, as does CRWTH (a type of stringed instrument). Both words are in MWCD10. They are pronounced "koom" and "krooth" (rhyming with room and truth). Other such words, not in MWCD10, are TWP (stupid), AWDL (an ode written in the strict alliterative meters), and LLWCHWR (a city-district in Wales). These words are of Welsh origin. The OED includes numerous archaic spellings in which W or V is a vowel.
The longest word in dictionaries having only one vowel is STRENGTHS.
PSYCHORHYTHMS (W2) is the longest word with only one vowel, ignoring Y [Stuart Kidd].
Some long common German words with only one vowel are SCHRUMPFST (you shrink; 10 letters), SCHRUMPFT (he shrinks; 9 letters), SCHWIMMST (you swim, informal, 9 letters) SCHWIMMT (he/she/it swims 8 letters), STRUMPF (stocking, 7 letters) [Gerd Baron, Robbie Ellis].
Some long words with only one vowel which is allowed to repeat are: BEEKEEPER, CHRONONHOTONTHOLOGOS (the title and hero of a 1734 burlesque tragedy by Henry Carey, used for “anyone who delivers an inflated address” —Brewer's Phrase and Fable), CURUCUCUS, DEFENSELESSNESSES, DEGENERESCENCE, DISINHIBITING, DUMBSTRUCK, EFFERVESCENCE, EKHETHEKHETHE (a place name in South Africa), ELSENERVELDENVEEN (a place name in the Netherlands), EYELETEERS (which is in OSW but I am unsure whether the Y is a vowel), GLYCYLS, HANDCRAFTSMAN, INSTINCTIVISTIC, KAWAKAWAMALAMALA (a place name in Fiji), KINNIKINNICKS, LIMLIMTIMIN (a place name in Papua New Guinea), LOXOLOPHODONTS, MARADANKADAWALAGAMA (a place name in Sri Lanka), MISSISSIPPI, MONOPHTHONGS, MUNDUNGUS, MYNYDDYSLWYN (a village in Yorkshire, England), NUMBSKULLS, OCONOMOWOC (a town in Wisconsin), PHILISTINISMS, POSTWORKSHOP, PRIMITIVISTIC, RETELEMETERED, RHYTHMS, SELF-CENTEREDNESSES, STRENGTHLESSNESSES, STRULDBRUGS, SUCCUBUS, SUSURRUS, TARAMASALATAS, TATHAGATAGARBHA, UNTRUTHFUL, USUFRUCT, WHIPSTITCHING.
In his book Language on Vacation, Dmitri Borgmann calls these words univocalics and lists SYMPHYSY as the longest Y-univocalic.
[The preceding section has contributions by Charles Turner, Marc Broering, Dan Tilque, Stuart Kidd, Philip Bennett].
Craig Rowland reports that in Quebec, there is a region known as the Outaouais, which, if in adjectival form, becomes lowercase, hence outaouais. The feminine form of this adjective is OUTAOUAISE, making it an eight-vowelled ten-letter word. He also says that in Quebecois French, the word for bullfrog is OUAOUARON, with six vowels in a row.
According to Paul Wright, the longest words with no vowels repeating are HYDROMETALLURGISTS (18 letters), HYDROMETALLURGIST (17 letters), and these 16-letter words: PLETHYSMOGRAPHIC, PSYCHOTHERAPISTS, and STADTHOLDERSHIPS.
OIOUEAE is one of the tropes or Gregorian formulas for the close of the lesser doxology in church music, representing the vowels in "World without end, Amen." [Music Lovers’ Encyclopedia (1954), by Rupert Hughes]
HÄÄYÖAIE, a Finnish word for "a plan for the wedding night," has 7 consecutive vowels, and 6 of the 8 vowel sounds that exist in Finnish [Tapio Tallgren]. However, Juha MÄkinen writes, "There exists another variant of this word body which has 8 consecutive vowels called RIIUYÖAIE. It means 'a plan for the night before a companionship begins...' Both words are very easily understood by a native Finnish speaking person."
In Spanish, REHUÍAOS has all five vowels pronounced, as the "H" is silent. It is a form of the verb rehuir (to avoid) and means "I/he/she/it avoided you" [Ignacio Fernández Galván].
In Hungarian, fiaiéi ("those belonging to his/her sons") has five vowels (and five syllables) and only one consonant [Ádám Szegi].
Gary Rosenberg suggests that QUACKSALVER and QUICKSILVER may be the longest pair of words related by changing two identical vowels to a different set of identical vowels.
OBAMA is the only last name of a President of the U. S. which begins and ends with a vowel.
MYTOXIA SEQUOIAE (a glowing millipede from California) has 15 letters, 10 of which are vowels. PORIA SEQUOIAE (redwood trunk rot) has 13 letters, 9 of which are vowels. [Charles Turner]
According to Ripley’s Believe It Or Not, the all-vowel sentence Aia ua ua o'o i eia aea a means “Don't you see how hard it is raining over yonder?” in the language of the Marquesas Islanders in the Pacific. [Paul Wright]
SOUTH AMERICA is the only continent with all 5 vowels in its name. EUROPE and ASIA are the only two continents which do not share a letter in their names. Between them they have all five vowels. [James A. Landau]