Polyhedra. Mitundu ya polyhedra ndi katundu

Polyhedra osati zatenga malo apamwamba mu masamu, komanso zimachitika tsiku ndi tsiku kwa munthu aliyense. Osati kutchula yokumba zinthu zokhudzana zosiyanasiyana polygons, kuyambira matchbox ndi mathero zinthu mapulani mu chikhalidwe kudzali makhiristo mu mawonekedwe a kyubu (mchere), prisms (galasi), piramidi (scheelite), octahedra (diamondi), etc. . d.

Lingaliro la polyhedron, mu mitundu Masamu polyhedrons

Masamu sayansi limapangidwa stereometry gawo limene limakamba ndi maonekedwe komanso katundu wa chochuluka mosiyanasiyana. Zojambula thupi mbali anapanga mu malo atatu azithunzi omwe tikunena njanjira ndi ndege (mbali) amadziwika ngati "polytopes". Mitundu ya polyhedra ali woposa oimira dazeni kwa chiwerengero zosiyana ndi mawonekedwe a nkhope.

Komabe, polyhedra zonse ndi katundu wamba:

1. Onsewo ali ndi zigawo zitatu yofunika: Nkhope (polygonal padziko), pamwamba (a kumathandiza kupeza ngodya zabwino kupangidwa mu nthaka mbali pawiri), ndi m'mphepete (mbali kapena kudula akalumikidzidwa anapanga pamphambano ya nkhope ziwiri).
2. Aliyense m'mphepete polygon zikugwirizana ndi awiri, ndi nkhope awiri okha amene poyerekezera ndi mzake ndi pafupi.
3. The lofufuma kwambiri mbali imodzi kumatanthauza kuti thupi kwathunthu anakonza mbali imodzi yokha ya ndege amene apuma mmodzi wa nkhope. ulamuliro ikugwira ntchito kwa nkhope zonse polyhedron lapansi. Izi akalumikidzidwa zojambula mu Masamu akuti olimba otchedwa otukukira kunja polyhedra. Kuchotserapo ndi stellate polyhedra amene anachokera ku matupi zonse polygonal zojambula.

Polyhedra angathe kugawidwa:

1. Mitundu ya polyhedra otukukira kunja, wopangidwa mwa makalasi zotsatirazi: ochiritsira kapena tingachipeze powerenga (a prism, piramidi, bokosi), pomwe (wochedwanso Plato zolimba), semiregular (wachiwiri dzina - Archimedean zolimba).
2. Non-otukukira kunja polyhedrons (stellate).

Prism ndi katundu

Masamu monga kugawikana Masamu amaphunzira katundu mosiyanasiyana atatu azithunzi omwe tikunena, mitundu ya polyhedra (prism pakati pawo). Prism otchedwa thupi zojambula zomwe wafuna nkhope ziwiri zofanana (wochedwanso zapansi) atagona ndege yomweyi, ndipo N-TH mbali nkhope mu mawonekedwe a parallelograms. Nawonso prism alinso mitundu ingapo, kuphatikizapo kotereku polyhedra, monga:

1. Parallelepiped - anapangidwa m'munsi ndi parallelogram - ndi polygon ndi awiriawiri yotsutsa kumathandiza kupeza ngodya ziwiri ofanana ndi mitundu iwiri iwiri ya zomenyanazo congruent.
2. Prism ndi perpendicular m'mphepete mwa tsinde la.
3. The prism okonda yodziwika ndi ngodya mosadziwika (ena kuposa 90) pakati pa nkhope ndi m'munsi.
4. Yoyenera yodziwika zapansi prism mu mawonekedwe a polygon zonse ndi mbali ofanana lateral.

The katundu waukulu prism ndi:

• Congruent zapansi.
• m'mbali zonse prism ndi ofanana ndi kufanana kwa wina ndi mzake.
• nkhope mbali zonse ndi mawonekedwe a parallelogram a.

piramidi

Piramidi otchedwa thupi zojambula kuti zizindikiro m'munsi ndi mmodzi wa N-TH wa nkhope triangular kuti kugwirizana pa mfundo limodzi - pamwamba. Tikumbukenso kuti ngati nkhope mbali ya piramidi awa akuimira Triangles chofunika, ndiye m'munsi angakhale ngati polygon triangular kapena quadrilateral ndi pentagonal, ndi zina zotero malonda infinitum. Pankhaniyi, dzina la piramidi limafanana ndi polygon pa maziko a. Mwachitsanzo, ngati tsinde ndi kansalu piramidi - piramidi triangular, quadrilateral - quadrangular, etc ...

Mapiramidi - izo konusopodobnye polyhedra. Mitundu ya polyhedra wa gulu limeneli, kuwonjezera pa pamwamba, mulinso oimira zotsatirazi:

1. Zonse piramidi ali maziko a munthu polygon zonse, ndipo msinkhu wake ali muno pakatikati pa bwalo alembedwa m'munsi kapena circumscribed mozungulira icho.
2. A piramidi amakona anayi aumbike pamene wina wa m'mphepete mbali intersect m'munsi pa mlingo woyenerera. Zikatero, m'mphepete woona uyu amatchedwanso piramidi msinkhu.

Piramidi katundu:

• Ngati kumene mbali zonse m'mbali congruent mapiramidi (kutalika yomweyo), iwo onse alipo m'munsi pa ngodya imodzi, ndi kuzungulira m'munsi akhoza kujambula bwalo ndi pakati imodzimodzi ndi ziyerekezo kwa vertex wa piramidi.
• Ngati m'munsi mwa piramidi ndi polygon zonse, m'mbali zonse lateral ndi congruent, ndi nkhope ndi isosceles Triangles.

Zonse polyhedron: zoyimira ndi katundu wa polyhedra

Mu stereometrical zatenga malo apadera thupi zojambula ndi ofanana kwathunthu kwa mbali mzake ndi mfundo imene chikugwirizana kwa nambalayi nthiti. Matupi amenewa amatchedwa zolimba Plato, kapena polyhedra zonse. Mitundu ya polyhedra ndi katundu zimenezi, pali kokha kanjedza zisanu:

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

dzina lake polyhedra zonse zifunika nzeru zapamwamba wakale Greek Plato anafotokoza matupi awa zojambula ntchito ndi kulumikiza ndi miyambo ya chikhalidwe: lapansi, madzi, moto, mpweya. Chachisanu chithunzi kupereka kufanana ndi loukitsa Akufa. Malinga ndi iye, masoka achilengedwe maatomu amafanana mitundu ya polyhedra zonse. Zikomo Mbali zake chochititsa chidwi kwambiri - chosokonekera, izi akalumikidzidwa zojambula chidwi kwambiri osati kwa masamu akale ndi nzeru ena, komanso mapulani, amisiri ndi Osema wa nthawi zonse. Kupezeka kwa mitundu 5 okha ndi mtheradi chosokonekera polyhedra ankaona anapeza achikhazikitso, iwo ngakhale kupereka mogwirizana ndi la Mulungu.

Hexahedron ndi katundu

Mu mawonekedwe a Amlowam'malo hexahedron Plato ankaganiza kufanana ndi kapangidwe ka atomu dziko lapansi. Kumene, tsopano kwathunthu anatsutsa amanena, amene Komabe, sikusokoneza ndi zojambula ndi modernity kukopa maganizo a kanjedza odziwika wa aesthetics wake.

Mu masamu, ndi hexahedron, iye ndi kyubu imatengedwa wapadera nkhani ya bokosi, amene nawonso, ndi mtundu wa prism. Choncho, katundu kugwirizana ndi katundu kyubu prism ndi kusiyana kokha kuti m'mbali zonse ndi m'mphambano za kyubu ali ofanana. Kuyambira lero katundu zotsatirazi:

1. Onse m'mbali mwa kyubu ali congruent ndi kugona mu ndege zikufanana ndi ulemu kwa wina ndi mzake.
2. nkhope zonse - congruent mabwalo (a kyubu of 6), aliyense amene angathe kumwedwa ngati maziko.
3. kumathandiza kupeza ngodya zabwino ndi ofanana intergranal 90.
4. Lililonse vertex ali ofanana nambala ya nthiti, ndicho 3.
5. The kyubu ali naini nkhwangwa chosokonekera, imene onse intersect pa nsonga ya mphambano ya diagonals wa hexahedron ndi, amatchedwa malo chosokonekera.

tetrahedron

Tetrahedron - ndi tetrahedron m'mbali ofanana mawonekedwe a Triangles, aliyense vertex amene ali Mphambano mfundo za m'mbali zitatu.

The katundu wa tetrahedron zonse:

1. nkhope zonse tetrahedron - ndi makona equilateral, kutanthauza kuti nkhope yonse ya tetrahedron ali congruent.
2. Popeza m'munsi ndi zonse zojambula chithunzi, ndiko kuti, ali mbali ofanana, nkhope za tetrahedron ndi converge pa ngodya chomwecho, i.e. kumathandiza kupeza ngodya zabwino ndi ofanana.
3. Kuchuluka planar kumathandiza kupeza ngodya iliyonse ya mfundo ndi wofanana 180, kuyambira kumathandiza kupeza ngodya onse ngofanana, mwanjila iliyonse ya tetrahedron zonse 60.
4. Aliyense wa mfundo imene mphambano mfundo misanje ya zosiyana (orthocenter) nkhope.

Octahedron ndi katundu

Pofotokoza mitundu ya polyhedra zonse, tisaiwale kuti chinthu monga octahedron, chimene akhoza zowoneka ankayimiridwa ngati awiri glued zapansi quadrilateral a mapiramidi zonse.

The katundu wa octahedron ndi:

1. Dzina la thupi zojambula limatiuza chiwerengero cha nkhope yake. Octahedron wapangidwa 8 congruent Triangles equilateral, omwe ndi ofanana ndi chiwerengero cha nkhope mfundo convergent, ndicho 4.
2. Popeza nkhope zonse octahedron ndi ofanana ndipo m'makona ake intergranal, omwe ndi 60, ndi Uwerenge planar kumathandiza kupeza ngodya iliyonse ya mfundo Choncho 240.

dodecahedron

Ngati ife kulingalira kuti nkhope yonse ya thupi zojambula ndi zonse Pentagon, inu mumatenga dodecahedron - chithunzi cha polygons 12.

Katundu dodecahedron:

1. Nthaŵi iliyonse vertex intersect pamodzi mbali zitatu.
2. nkhope onse ndi ofanana ndipo ndi kutalika nthiti, ndi malo ofanana.
3. Pa dodecahedron ndi nkhwangwa 15 ndipo ndege chosokonekera, ndi aliyense wa iwo umadutsa pakatikati pa nkhope pamwamba ndi m'mphepete zosiyana.

icosahedron

Mofanana chidwi kuposa dodecahedron, icosahedron chithunzi umaimira atatu azithunzi omwe tikunena zojambula thupi 20 ndi mbali ofanana. Pakati katundu icosahedron zabwino otsatirawa:

1. nkhope zonse icosahedron wa - isosceles Triangles.
2. Nthaŵi iliyonse vertex wa polyhedron ndi converge nkhope zisanu, ndi Uwerenge kumathandiza kupeza ngodya pafupi ndi nsonga 300.
3. Icosahedron n'chimodzimodzi ndi dodecahedron, nkhwangwa 15 ndipo ndege chosokonekera kudutsa mfundo pakati pa zomenyanazo.

polygons semiregular

Komanso zolimba Plato, polyhedrons otukukira kunja gulu mulinso zolimba Archimedean, amene truncated polyhedrons zonse. Mitundu ya polyhedra mu gulu ili ndi katundu zotsatirazi:

1. thupi zojambula ndi pairwise ofanana nkhope ya mitundu yosiyanasiyana, mwachitsanzo, truncated tetrahedron n'chimodzimodzi ndi tetrahedron zonse, 8 nkhope, koma ngati thupi 4 Archimedean nkhope ndi triangular mphako and 4 - hexagonal.
2. kumathandiza kupeza ngodya zabwino ndi congruent kuti vertex wina.

stellate polyhedra

Oimira mitundu neobomnyh matupi geometrical - polyhedrons stellate, nkhope yomwe intersect ndi mzake. Iwo akhoza kupangidwa ndi pophatikizana a zonse matupi awiri kapena atatu azithunzi omwe tikunena kapena chifukwa cha kupitiriza nkhope zawo.

Motero, yodziwika stellate polyhedra monga: mawonekedwe stellate wa octahedron ndi, dodecahedron, icosahedron, cuboctahedral, icosidodecahedron.