Polyhedra. Types of polyhedra le thepa tsa bona

Polyhedra se feela lula sebakeng se hlaheletseng le geometry, empa hape etsahala bophelong ba letsatsi le letsatsi le leng le motho. A se ke a letho ka maiketsetso lintho tse amanang le ho mefuta e fapaneng ya dikhutlontsi, ho qala ho tswa ho matchbox ka le ho ipolaea likarolo meralo le linthong tsa tlhaho e boetse e hlaha kristale ka mokgwa wa sekotwaneng (letsoai), diporisimi (kristale), phiramiti (scheelite), octahedra (taemane), joalo-joalo .: d.

Khopolo ea polyhedron, ka mefuta le geometry tsa polyhedrons

Lipalo, geometry saense e kenyelletsa ditokiseletso stereometry karolo tse sebetsanang le litšobotsi le thepa ya bongata dibopeho. Thutatekanyo 'mele mahlakoreng li thehoa sebaka tse tharo-tlhakore potapotoeng ke lifofane (litšobotsi tse) di a tsejoa e le "polytopes". Types of polyhedra o fetang le baemeli ba dozen ya nomoro tšoaneng le sebōpeho sa lifahleho tsa.

Leha ho le joalo, polyhedra kaofela ba na le thepa ea ho tloaelehile hore batho:

1. Kaofela ba na le metsoako e meraro ea bohlokoa: sefahleho (polygonal holim'a), ka holimo (le dikhutlo thehoa fatše litšobotsi tse komponeng), e bohale (lehlakoreng kapa khaola tsa dibopeho tse thehoa ka mateano sa lifahleho tse peli).
2. E mong le e bohale khutlontsi kopanya tse peli tse, le lifahleho tse peli feela tse mabapi le mong ho e mong tse haufi.
3. The bulge bolela hore 'mele oa ka ho feletseng o ile a lokisetsa ka lehlakoreng le leng feela la sefofane leo e itšetlehile e mong oa le lifahleho. puso ea sebetsa ho lifahlehong tsohle tsa polyhedron ena. Tsena tsa dibopeho tse thutatekanyo ka lipalo, geometry poleloana e reng tiileng bitsoa khonvekse polyhedra. Ntle le mabaka a ba stellate polyhedra tse tswang mele kamehla polygonal thutatekanyo.

Polyhedra ka aroloa:

1. Types of polyhedra khonvekse, e bopilweng ka ba le litlelase tsa ho latelang: tloaelehileng kapa khale (a porisime, phiramite, lebokose), le letona (boetse o bitsoa ba ise ba nyalane-butle), semiregular (bobeli lebitso la - Archimedean-butle).
2. Bao e seng khonvekse polyhedrons (stellate).

Porisime le thepa ea eona

Lipalo, geometry ka karohano le geometry ithuta thepa ya dibopeho tse tharo-tlhakore, mefuta ya polyhedra (porisime har'a bona). Porisime bitsoa 'mele thutatekanyo eo e hlokahalang lifahleho tse peli le tsoanang (eo hape a bitsoang makalana) rapaletse lifofane tšoanang le eo,' me a n g-go th oa lehlakoreng tobaneng le ka mokgwa wa parallelograms. Ka lehlakoreng le leng, porisime boetse e na le mefuta e sa tsoaneng 'maloa, ho akarelletsa le mefuta e joalo ea polyhedra, tse kang:

1. Parallelepiped - thehoa ha e le setsi ke pharallelokeramo - e khutlontsi le lipara tsa hanyetsa dikhutloteng tse peli tse lekanang le lipara tse peli ya mahlakoreng a mabeli dipopotshwano.
2. Porisime ke perpendicular ho molekeng oa botlaaseng.
3. The porisime sekametse tšoauoa ka hlaha ka lehlakoreng le sa tobang (ntle le 90) pakeng tsa lifahleho le e le setsi.
4. Tšoanetseng tšoauoa makalana porisime ka mokgwa wa e khutlontsi kamehla le mahlakoreng lekanang lateral.

The thepa ka sehloohong sa porisime ho:

• Dipopotshwano makalana.
• ea metshetshe kaofela porisime ba lekanang le e tšoanang le mong ho e mong.
• lifahleho lehlakoreng tsohle ho ba le sebopeho sa pharallelokeramo ka.

phiramiti

Phiramiti bitsoa 'mele thutatekanyo hore kenyelletsa ditokiseletso e botlaaseng le e mong oa' n '-th, ba lifahleho kgutlotharo hore hokela ka nako e le' ngoe - hodimo. Re lokela ho hlokomela hore ha lifahleho lehlakoreng la phiramiti ba emeloang ke dikhutlotharo hlokahala, ka nako eo e le setsi ka tšoana le khutlontsi kgutlotharo kapa sekhutlonne le pentagonal, joalo-joalo papatso infinitum. Tabeng ena, lebitso la phiramiti e tšoana le e khutlontsi ka botlaaseng. Ka mohlala, haeba e le setsi ke triangolo phiramiti - phiramite kgutlotharo, sekhutlonne - quadrangular, joalo-joalo ...

Liphiramide - e konusopodobnye polyhedra. Types of polyhedra tsa sehlopha sena, ho phaella ho tse ka holimo, o ne a boetse a akarelletsa baemeli latelang:

1. Kamehla phiramiti na motheo wa ka khutlontsi kamehla, 'me bophahamo ba eona e e thulametse ho e le setsi sa le selikalikoe ngotsoe botlaaseng kapa maemo ho potoloha.
2. A phiramiti ya khutlonnetsepa Ho thehoa ha e mong oa metshetshe lehlakoreng intersect botlaaseng nakong e hlaha ka lehlakoreng le letona. Boemong bo joalo, bohale ena ea 'nete o boetse o bitsoa phiramiti bophahamo.

Phiramiti Properties:

• Tabeng ea moo lehlakoreng tsohle metshetshe dipopotshwano liphiramide (bophahamo tšoanang), kaofela ba ile ba lepelela le botlaaseng e ka hlaha ka lehlakoreng le le leng, 'me ho pota botlaaseng ka atamela e le selika-likoe ka setsi coinciding le boqapi ba vertex tsa phiramiti ena.
• Ha e le setsi sa phiramiti le ke khutlontsi kamehla, metshetshe tsohle lateral ke dipopotshwano, 'me lifahleho tsa ba isosceles kgutlotharo.

Kamehla polyhedron: mefuta e le thepa ya polyhedra

Ka stereometrical lula sebakeng se khethehileng 'mele thutatekanyo ka lekanang ka ho feletseng ho litšobotsi tse e mong le tse ling tse le divertise ea eona e amanang le palo e tšoanang ea likhopo. Tsena 'mele ba bitsoa-butle ba ise ba nyalane, kapa polyhedra kamehla. Types of polyhedra le thepa e joalo, ho na le feela lipalo tse hlano:

1. Tetraheterone.
2. Hexahedron.
3. Octahedron.
4. Dodecahedron.
5. Icosahedron.

lebitso la hae polyhedra kamehla lokela ho bo-rafilosofi ba boholo-holo Segerike Plato o ile a hlalosa lihloliloeng tsena tsa thutatekanyo ka mosebetsi oa bona le ho hokahanya bona le thepa ea motheo ha ea tlhaho: mobu, metsi, mollo, moea. Bohlano palo fuoa ho tšoana le sebopeho oa bokahohle. Ho ea ka eena, likoluoa tsa tlhaho liathomo tšoana le mefuta e meng ea polyhedra kamehla. Thanks ho tšobotsi lona ho fetisisa e hlollang ka botle - setshwani, tsena tsa dibopeho tse thutatekanyo la thahasello e khōlō eseng feela bakeng sa thuto ea lipalo le ea boholo-holo le bo-rafilosofi, empa le bakeng sa Litsebi, painters le sculptors ya nako tsohle. Ho ba teng ha mefuta e 5 feela le ka ho feletseng setshwani polyhedra nkoa e sibolloa motheo, ba bile ba fuoa mabapi le tsela ea bomolimo ea.

Hexahedron le thepa ea eona

Ka mokgwa wa ke bahlahlami hexahedron Plato nahana tšoana le sebopeho sa ea liathomo lefatše. Ya e le hantle, hona joale ka ho feletseng a hanyetsa khopolo ena, eo, leha ho le joalo, ha e kena-kenana le litšoantšo le bokoli ho hohela likelello tsa lipalo tsebahalang ea aesthetics ea hae.

Ka lipalo, geometry, e hexahedron, o ile a ba modisekwere, seraro ho nkoa e khethehileng tabeng ea lebokoseng, e leng, le eena, ke mofuta oa porisime. Ka lebaka leo, thepa e amanang le thepa sekotwaneng porisime le phapang feela hore metshetshe tsohle le likhutlong tsa sekotwaneng sa baa lekana. From ena le thepa tse latelang:

1. All molekeng oa sekotwaneng sa di dipopotshwano le leshano ka lifofane e tšoanang mabapi le mong ho e mong.
2. lifahlehong tsohle - dipopotshwano dikwere (tsa sekotwaneng sa 6), leha e le efe ea eona e ka nkoa e le motheo oa.
3. dikhutloteng tsohle baa lekana intergranal 90.
4. Le e mong le vertex na e lekanang palo ea likhopo, e leng 3.
5. The sekotwaneng na robong lilepe tsa setshwani, eo ka eona bohle intersect a le makhatheng a mateanong a litsela tsa diagonals tsa hexahedron ea, o ile a re e le setsi sa setshwani.

tetraheterone

Tetraheterone - e tetraheterone ka metshetshe lekana ka sebopeho sa dikhutlotharo, e mong le e vertex ea eo ke mateano ntlha ea metshetshe tse tharo.

The thepa ya tetraheterone kamehla:

1. lifahleho kaofela tetraheterone - e triangolo matlhakore aa lekanang, e leng se bolelang hore ka lifahlehong tsohle tsa tetraheterone e ke dipopotshwano.
2. Ho tloha e le setsi ke kamehla thutatekanyo palo, ke hore, ho na le mahlakoreng lekana, lifahleho tsa tetraheterone le converge ka hlaha ka lehlakoreng le e tšoanang, i.e. dikhutloteng tsohle baa lekana.
3. Palo planar dikhutloteng ka mong le e mong divertise le o lekana le 180, ho tloha mahlakoreng tsohle baa lekana, angle efe kapa efe ya e tetraheterone kamehla 60.
4. E mong le e ba divertise thulametse motsoako ntlha libaka tse phahameng tsa se fapaneng (orthocenter) sefahleho.

Octahedron le thepa ea eona

Ha a hlalosa mefuta polyhedra kamehla, re lokela ho hlokomela hore ntho e octahedron e, e leng e ka pono hlahisoa e le tse peli tse lamellar makalana sekhutlonne ea liphiramide kamehla.

The thepa ea octahedron ho:

1. Lebitso la 'mele thutatekanyo bolella palo ea lifahleho tsa lona. Octahedron entsoe 8 dipopotshwano dikhutlotharo matlhakore aa lekanang, e mong le e ba e lekana le palo ea lifahleho divertise convergent, e leng 4.
2. Ho tloha ka lifahlehong tsohle tsa octahedron ba lekanang le likhutlong tsa lona intergranal, mong le e mong eo e ka bang 60, 'me o bala planar dikhutloteng efe kapa efe ya divertise Kahoo 240.

dodecahedron

Haeba re nahana hore lifahlehong tsohle tsa 'mele tsa thutatekanyo ke kamehla khutlotlhano, o fumana dodecahedron - mokhabo-dikhutlontsi 12.

Properties dodecahedron:

1. Ha e mong le e vertex intersect hammoho mahlakoreng a mararo.
2. lifahlehong tsohle baa lekana 'me ba na le nako e lekanang ea likhopo,' me sebakeng sa lekanang.
3. Ka dodecahedron sa lilepe 15 le lifofane tsa setshwani, ka leha e le efe e 'ngoe ea tsona e ntse e feta ka bohareng ba sefahleho holimo le e bohale fapaneng.

icosahedron

Ka tsela e tsoanang thahasellisang ho feta dodecahedron, icosahedron palo emela mahlakore a mararo tsa thutatekanyo 'mele 20 le mahlakoreng lekanang. Har'a thepa e icosahedron tokelo tse latelang:

1. lifahlehong tsohle tsa icosahedron e - isosceles kgutlotharo.
2. Ha e mong le e vertex tsa polyhedron le converge lifahleho tse hlano, 'me o bala dikhutloteng haufi ke litlhōrō 300.
3. Icosahedron ho tšoana le ho le dodecahedron, lilepe 15 le lifofane tsa setshwani feta lintlha tse bohareng ba mahlakoreng a mabeli.

dikhutlontsi semiregular

Ho feta moo-butle ise ba nyalane, polyhedrons khonvekse sehlopha e boetse e akarelletsa-butle Archimedean, tse truncated polyhedrons kamehla. Types of polyhedra sehlopheng sena ba le thepa tse latelang:

1. 'mele thutatekanyo ke pairwise lekanang lifahleho tsa mefuta e' maloa, ho etsa mohlala, truncated tetraheterone ho tšoana le ho ka tetraheterone kamehla, 8 lifahleho, empa tabeng ea 'mele 4 Archimedean lifahleho tse likhutlo li tharo e bopehileng le 4 - hexagonal.
2. dikhutloteng tsohle di dipopotshwano ho vertex ngoe.

stellate polyhedra

Baemeli ba mefuta neobomnyh mele jeometeri - polyhedrons stellate, lifahleho tseo intersect le mong ho e mong. Ba ile ba ka etsoa ke tshwaragano ba kamehla 'mele e' meli e meraro-tlhakore kapa ka lebaka la ho tsoela pele sa lifahleho tsa tsona.

Ka tsela eo, tse kang e ileng ea tsejoa stellate polyhedra kang: sebopeho stellate tsa octahedron e, dodecahedron, icosahedron, cuboctahedral, icosidodecahedron.