I-Polyhedra. Izinhlobo ze-polyhedra nezakhiwo zazo

I-Polyhedra ingagcini nje indawo evelele ku-geometry, kodwa futhi ikhona empilweni yansuku zonke yomuntu ngamunye. Ngaphandle kokusho izinto ezidalwe ngokusetshenziswa kwansuku zonke ngendlela yama-polygons ahlukahlukene, eqala ngebhokisi lokufanisa futhi ephela ngezakhi zokwakha, emvelweni kukhona amakristalu ngendlela ye-cube (usawoti), ama-prism (crystal), ama-pyramid (i-scheelite), i-octahedra (idayimane) kanye n E.

Umqondo we-polyhedron, izinhlobo ze-polyhedra nge-geometry

I-geometry njengesayensi iqukethe isigaba se-stereometry esihlola izici kanye nezakhiwo zezibalo ezintathu-ntathu . Imizimba ye- geometri , izinhlangothi zazo ezingxenyeni ezintathu-ntathu zakhiwa yizindiza eziboshiwe (ubuso), zibizwa ngokuthi "polyhedra." Izinhlobo ze-polyhedra inombolo engaphezu kweyishumi nambili abameleli, ezihlukile kwinombolo nesimo sobuso.

Noma kunjalo, wonke ama-polyhedra anezinto ezivamile:

1. Zonke zinezingxenye ezintathu ezibalulekile: ubuso (i-polygon surface), i-vertex (emagumbini akhiwe emhlangothini wobuso), umkhawulo (ohlangothini lwesibalo noma ingxenye eyakhiwe ekuhlanganiseni kobuso ababili).
2. Umngcele ngamunye we-polygon ujoyina ezimbili, futhi ubuso ababili kuphela obuseduze komunye nomunye.
3. I-Convexity isho ukuthi umzimba utholakale ngokuphelele kuphela ohlangothini olulodwa lwezindiza lapho omunye obuso obukhona khona. Umthetho usebenza kuwo wonke ubuso we-polyhedron. Izibalo zejometri ezinjalo ku-stereometry zibizwa ngokuthi i-convex polyhedra. Okungaphandle kwenkanyezi ye-polyhedra, eyakhiwa yizindikimba ezivamile ze-polyhedral geometric.

I-Polyhedra ingahlukaniswa ibe yi:

1. Izinhlobo ze-convex polyhedra eziqukethe amakilasi alandelayo: ezijwayelekile noma zakudala (i-prism, i-pyramid, i-parallelepiped), ejwayelekile (ebizwa nangokuthi izigungu ze-Platon), okujwayelekile (igama lesibili - imizimba ye-Archimedean).
2. I-nonconvex polyhedra (stellate).

I-Prism nezakhiwo zayo

I-stereometry njengengxenye ye-geometry ihlola izindawo zezinombolo ezintathu, izinhlobo ze polyhedra (i-prism enombolweni yabo). I-prism yumzimba we-geometric ophethe izithombe ezimbili ezifanayo ngokuphelele (ezibizwa nangokuthi izinsika) ezilele ezindizeni ezifanayo, nenombolo ye-n-th yobuso be-lateral ngendlela yama-parallelograms. Kanti, i-prism inezinhlobo eziningana, kufaka phakathi izinhlobo ezinjalo ze-polyhedra njenge:

1. I-Parallelepiped - ifakwe uma kukhona i-parallelogram esisekelweni - i-polygon enezinhlangothi ezimbili ezilinganayo ezilingene nezilinganiso eziphambene nezinhlangothi zombili ezihlangene.
2. I-prism eqondile inemiphetho ehamba phambili kuya kwesisekelo.
3. I-prism esithambekeleyo ibonakala ngokuba khona kwama-angles ngqo (ngaphandle kuka-90) phakathi kobuso nesisekelo.
4. I-prism efanele ibonakala ngezisekelo ezinjenge-polygon ejwayelekile ebusweni obulinganayo.

Izakhiwo eziyisisekelo ze-prism:

• Izisekelo eziyisisekelo.
• Zonke izingxenye ze-prism zilingana futhi zifana nomunye nomunye.
• Zonke ubuso be-lateral zinesimo se-parallelogram.

I-Pyramid

Iphiramidi iyigumbi lejometri eliqukethe isisekelo esisodwa nenombolo ye-n-th yobuso obunxantathu ejoyina iphuzu elilodwa - i-vertex. Kumele kuqashelwe ukuthi uma ubuso obunamapiramidi buboniswa yizintathu, khona-ke ngaphansi kwesibhakabhaka kungaba khona i-polygon ye-triangular, i-quadrilateral, ne-pentagon, njalonjalo ne-ad infinitum. Igama lepiramidi lizohambisana ne-polygon ngezansi. Isibonelo, uma kukhona unxantathu phansi kwephiramidi, iphiramidi encane, i-quadrilateral i-quadrangular, njalonjalo.

Amapiramidi angama-polyhedra. Izinhlobo ze-polyhedra zaleli qembu, ngaphandle kwalokhu ngenhla, zihlanganisa nalabo abalandelayo:

1. Ipiramidi evamile ine- polygon ejwayelekile phansi , futhi ukuphakama kwayo kufakwe phakathi kwendilinga ebhalwe phansi noma echazwe nxazonke.
2. I-pyramid ephindaphindiwe isakhiwe lapho enye yezingxenyeni ezisemuva ijikeleza ngesisekelo esingakwesokudla. Kulesi simo, lo mgqa ubizwa nangokuthi ukuphakama kwepiramidi.

Izakhiwo zepiramidi:

• Uma zonke izingxenyeni ezisemuva zephiramidi zihlanganiswa (ngokuphakama okufanayo), khona-ke zonke zihlangene ngesisekelo ngehora elilodwa, futhi zizungeza isisekelo ongayidonsa umbuthano ngesikhungo esivumelana nokubonakala kwephezulu kwepiramidi.
• Uma kukhona i-polygon ejwayelekile phansi kwepiramidi, ngakho-ke yonke imiphetho yesikhashana ihlanganiswa, futhi ubuso bubuncane be-isosceles triangles.

Lungisa i-polyhedron: izinhlobo nezindawo ze-polyhedra

Esikhathini se-stereometry, indawo ekhethekile igcwele imizimba ye-geometri enezinhlangothi ezilinganayo ngokuphelele, lapho ama-edges anjalo afakwa khona. Lezi zidumbu zibizwa ngokuthi izidumbu zePlaton, noma i- polyhedra evamile. Izinhlobo ze-polyhedra nalezi zakhiwo zinamanani amahlanu kuphela:

1. I-tetrahedron.
2. I-hexahedron.
3. Octahedron.
4. I-dodecahedron.
5. Icosahedron.

Ngegama labo, i-polyhedra elungile ingenxa yesazi sefilosofi esingumGreki uPlato, owachaza lezi zidumbu ze-geometric emisebenzini yakhe futhi wazixhuma ngezinto eziphilayo: umhlaba, amanzi, umlilo, umoya. Isibalo sesihlanu sanikezwa ukufana nesakhiwo sezulu. Ngokombono wakhe, ama-athomu ezakhi zemvelo afana nokuma izinhlobo ze-polyhedra ejwayelekile. Ngenxa yempahla yayo ekhangayo kakhulu - ukulinganisa, lezi zikhungo ze-geometri zazinesithakazelo esikhulu hhayi kuphela kubabalo bezibalo nezazifilosofi zasendulo, kodwa nakwabakhi, abadwebi nabadwebi bezikhathi zonke. Ukuba khona kwezinhlobo ezingu-5 kuphela ze-polyhedra ezinokulinganisa okuphelele kwakubhekwa njengokutholwa okuyisisekelo, baze baze banikezwe ukuxhumana nokuqala okuvela kuNkulunkulu.

I-hexahedron nezindawo zayo

Esimweni se-hexagon, abazuzi bakaPlato bafana nokuhlelwa kwama-athomu omhlaba. Yiqiniso, okwamanje leli cwaningo liphikisiwe ngokuphelele, okuyinto, noma kunjalo, elingavimbeli lezi zibalo ukuba zingadonseli izingqondo zamanani awaziwa kakhulu ku-aesthetics yabo.

E-geometry, i-hexahedron, futhi i-cube, ibhekwa njengesimo esithile se-parallelepiped, okuyinto efana ne-prism. Ngakho-ke, izakhiwo ze-cube zihlobene nezakhiwo ze-prism ngenani elilodwa kuphela ukuthi wonke ubuso nama-angles we-cube alingana nomunye nomunye. Lokhu kusho izakhiwo ezilandelayo:

1. Zonke izingxenye ze-cube zihlangene futhi zilele ezindizeni ezifanayo ngokuphathelene nomunye nomunye.
2. Zonke ubuso zindawo ezigcwala (kunezingu-6 ku-cube), noma yiziphi zazo ezingathathwa njengesisekelo.
3. Zonke izingalo zokuxhumana zilingana no-90.
4. Kusukela ku-vertex ngayinye kulandela inani elilinganayo lemiphetho, okuyi-3.
5. I-cube inezinhlayiyana ezingu-9 ze-symmetry, zonke ezihlangene emkhakheni wezinhlangothi ze-diagonals ze-hexahedron, okuthiwa yi-center of symmetry.

I-tetrahedron

I-tetrahedron iyinetrahedron enezinhlangothi ezilinganayo ezinjenge-triangles, ngasinye esinesigcawu sayo siyisici sokuxhuma ubuso obuthathu.

Izakhiwo zetrahedron ejwayelekile:

1. Konke ubuso be-tetrahedron kukhona izinhlanzi ezilinganayo, okulandela ukuthi bonke ubuso be-tetrahedron bahlangene.
2. Njengoba isisekelo sibhekiswe kumuntu ovamile we-geometric figure, okungukuthi, unezinhlangothi ezilinganayo, khona-ke ubuso bukaTetrahedron buya ekhoneni elifanayo, okungukuthi, zonke izingalo zilingana.
3. Isamba se-planar angles ngayinye yama-vertic ayi-180, ngoba zonke izingalo zilingana, ngakho-ke noma yikuphi ukuma kwe-tetrahedron ejwayelekile kungama-60.
4. Ngamanye ama-vertic ahlongozwa ekhoneni lezinhlangothi zokuphakama kwebuso obuhlukile (orthocenter).

I-Octahedron nezindawo zayo

Lapho ichaza izinhlobo ze-polyhedra ejwayelekile, umuntu akanakuhluleka ukuphawula into enjenge-octahedron engabonakala ngokumelela ngendlela yama-pyramid emibili ejwayele ukuhlanganiswa ndawonye ngezinyawo.

Izakhiwo ze-octahedron:

1. Igama legumbi lejometri lisitshela inombolo yobuso bayo. I-octagon iqukethe ama-triangles angu-8 e-congruent equilateral, ku-vertex ngayinye ekhona inani elilingana lobuso, okuyi-4.
2. Njengoba zonke ubuso bomuntu o-octahedron zilingana, ama-angle angaphakathi, angalingana no-60, alinganisiwe, kanti inani lama-plan angama-vertices, ngakho-ke, angu-240.

I-dodecahedron

Uma sicabanga ukuthi bonke ubuso begumbi lejometri liyi- pentagon ejwayelekile, sithola i-dodecahedron - isibalo sama-polygoni angu-12.

Izakhiwo ze-dodecahedron:

1. I-vertex ngayinye ibheka ubuso abathathu.
2. Zonke ubuso zilingana futhi zinebude obufanayo bomkhawulo, kanye nendawo elinganayo.
3. I-dodecahedron inezinhlayiyana ezingu-15 nezindiza zokulinganisa, futhi noma yiziphi zazo zidabula i-vertex ebusweni naphakathi komkhawulo ohlukile.

Icosahedron

Okungathandeki okuncane kune-dodecahedron, i-icosahedron iyinhlangano ebalulekile yejometri enebuso obulinganayo obungama-20. Phakathi kwezakhiwo ze-dentagon ejwayelekile, okulandelayo kungaphawulwa:

1. Bonke ubuso be-icosahedron yizintathu ze-isosceles.
2. I-vertex ngayinye ye-polyhedron iguqula ubuso obunhlanu, futhi inani lama-vertex angles angama-300.
3. I-icosahedron ine, njenge-dodecahedron, ama-axe angu-15 kanye nezindiza zokulinganisa ezidlula ezindaweni ezibhekene nazo.

Ama-polygoni ajwayelekile

Ngaphandle kwama-solids asePlatoli, iqembu le-convex polyhedra lihlanganisa nezidumbu ze-Archimedean, ezithathwa ngama-polyhedra avamile. Izinhlobo ze-polyhedra zaleli qembu zinempahla elandelayo:

1. Imizimba ye-geometri ibe nombuso olinganayo wezinhlobo eziningana, isibonelo, i-tetrahedron esinezintathu inezintambo ezingu-8 kanye ne-tetrahedron ejwayelekile, kodwa esimweni somzimba we-Archimedean 4 ubuso buzobe buyingqayizivele futhi bube ngu-4 - hexagonal.
2. Wonke ama-angles we-vertex eyodwa ahlangene.

I-star polyhedra

Abamele izinhlobo ezingekho zezinto ze-geometric kukhona inkanyezi ye-polyhedra obuso babo babhekana. Zingakhiwa ukuhlanganiswa kwemizimba emibili ejwayelekile emibili noma ngenxa yokuqhubeka kobuso babo.

Ngakho-ke, le nkanyezi ye-star polyhedra njengoba eyaziwa: i-octahedron ene-star, i-dodecahedron, i-icosahedron, i-cuboctahedral, i-icosododecedhedron.