Polyhedra. Ano o ka polyhedra a me ko lakou mau waiwai

Polyhedra Mai noho wale i ke koʻikoʻi wahi ma ka anahonua, akā, no hoi ana i loko o ka maʻamau o ke ola o na kanaka. Not e hōʻike i kaʻimi hoʻopunipuni pili ikamu i loko o ka likeʻole ma o polygons, e hoʻomaka ana mai o ka matchbox a pau kuhikuhipuʻuone nā kumumea i loko o ke ano maoli no hoi ana nā pōaka i loko o ka palapala o ke kupa (paʻakai), prisms (aniani), pyramid (scheelite), octahedra (daimana), etc. . d.

I ka manaʻo o ka polyhedron, ma ka anahonua ke ano o polyhedrons

Anahonua 'epekema maupaʻa stereometry pauku e epa me nā' ano a me ka waiwai o bulk kinona. Geometric kino aoao i hanaʻia i loko o ekolu-dimensional makahiki kau palena ia ana e Kekoa (facets) e ike ia "polytopes". Ano o ka polyhedra ua oi ma mua o ke kakini ka poeikohoia o ka like pu ole, ka helu a me ka shape o ka maka.

Aka hoi, a pau polyhedra i na waiwai:

1. I mai la lakou a pau i ekolu integral eiiiiiaiou: ka maka (polygonal ili), ka luna (ka pana pua i hanaʻia i loko o ka lepo facets hui), he maka (ʻaoʻao a okioki ano i hanaʻia ma ka huina o nā maka).
2. Kēlā me kēia iieeaii palena hoʻohuiʻia ka mau, a me nā makaʻelua wale i ka mea ma ka pili ana i kekahi i kekahi mea e pili.
3. Ke bulge o ia hoʻi, i ke kino ua pau ka hooponopono ia ma kekahi wale nōʻaoʻao o ka pelane ma iʻanuʻu kekahi o na maka. Ka rula i pili i nā maka o ka polyhedron. Mau geometric kinona i paa anahonua manawa kapa convex polyhedra. 'Ia i stellate polyhedra i i loko mai o ka pololei, polygonal geometric kino.

Polyhedra hiki ke maheleia i:

1. Kind o convex polyhedra, oia no ka mea kēia mau papa:ʻike mau ole Classic (he prism, he pyramid, he pahu), pono (i kapaʻia Platonic puaʻa hiwa), semiregular (lua o ka inoa - Archimedean puaʻa hiwa).
2. Ole-convex polyhedrons (stellate).

Prism a me kona waiwai

Anahonua like me ka mahele anahonua haʻawina i nā waiwai o ka ekolu-dimensional ano, ke ano o ka polyhedra (prism mawaena o lakou). Prism kapaia geometric kino i i koi 'ia elua'ālike maka (i kapaʻia ko lākou mau kumu), e moe ana ma ka laua Kekoa, a me N-la o kaʻaoʻao maka i loko o ka palapala o parallelograms. I huli ai oe, o ka prism i loaʻa paha kekahi mauʻano likeʻole, a me na ano o ka polyhedra, e like me:

1. Parallelepiped - i hana ia i ke kumu o ka parallelogram - he iieeaii me ka hui o nā kue like pana pua a me nā hui o ke alo oʻaoʻao congruent.
2. Prism mea p ÷ haku i na kihi o ka waihona ipu.
3. Kaʻiʻini prism wehewehe aku ma kaʻauhau'ēʻaʻe huina ( 'ē aʻe ma mua o 90) ma waena o ke alo a me ke kumu.
4. Kupono wehewehe aku prism kumu i loko o ka palapala o ka papa iieeaii me ka like kīloi paʻewa aoao.

Ke kumu waiwai o ka prism:

• Congruent kumu.
• na kihi a pau o ka prism e kau like, a ia laua i kekahi i kekahi.
• Allʻaoʻao maka i ke kinona o ka parallelogram.

pyramid

Pyramid kapaia geometric kino e maupaʻa i ke kumu a me kekahi o ka N-la o ka triangular maka e hoʻohui i ka hookahi wahi - ka luna. It E e kaulana ia ina kaʻaoʻao maka o ka pyramid i na poe e triangle mauna ua koi 'ia, a laila, i ke kanaka hewa ke e, e like me ka triangular iieeaii a quadrilateral a me ka pentagonal, a no laila, ma luna a infinitum. Ma keia hihia, hoʻopili like i ka iieeaii ma ke kumu o ka inoa o ka pyramid. No ka laʻana, ina ke kumu o ka triangle pyramid - he triangular pyramid, quadrilateral - quadrangular, a pela aku ...

Pyramids - ia konusopodobnye polyhedra. Ano o ka polyhedra o keia pae, ma ka hou ana i na luna, i loaʻa ka mea, penei ka poeikohoia:

1. Ka pololei, pyramid i kumu o ka regular iieeaii, a me ka uaʻana o kona kiekie i ka waenakonu o ka p ÷ ai kākauʻia i loko o ka waihona ipu a circumscribed a puni ia.
2. A huinahń pyramid ua hanaʻia ka wā kekahi o kaʻaoʻao kihi intersect i ke kumu ma ka huina akau. Ma ia ka hihia, kapaʻia kēia kihi oiaio no hoi pyramid kiʻekiʻe.

Pyramid waiwai:

• Ma ka hihia ma kaʻaoʻao a pau kihi congruent pyramids (ke ki eki e), ka mea a pau ano me ke kumu i kekahi huina, a puni ke kumu ke unuhi i ka p ÷ ai me ka piko coinciding me ka wānana o ka vertex o ka pyramid.
• Inā i ke kumu o ka pyramid mea he regular iieeaii, a pau kīloi paʻewa kihi i congruent, a me na maka i isosceles triangle mauna.

Ka pololei, polyhedron: ano a me ka waiwai o ka polyhedra

Ma stereometrical kūlana 'i kūikawā wahi ka geometric kino me ka pono like i kēlā me kēia' ē aʻe facets na vertices o i ua pili i ka mea hookahi helu o ka iwi aoao. Mau kino i kapaia Platonic puaʻa hiwa, a me ka pololei, polyhedra. Ano o ka polyhedra me ka waiwai, eia wale elima huahelu:

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

Kona inoa regular polyhedra e koi 'ia i kahiko Greek poe akeakamai Plato ho'ākāka' ia ma kēia mau geometric kino i loko o kā lākou hana, a, e hoʻohui iā lākou i nā kumu o ke ano maoli: honua, ka wai, ke ahi, ea. Lima o ka huahelu i hookoia mea like me ka 'ole o ka ke ao holoʻokoʻa. E like me ia ia ia, ma kona ano maoli i na ino nā'ātoma e hoohalike ai i keʻano o ka maʻamau polyhedra. Mahalo i kona loa nui hiʻona - symmetry, mau geometric kinona o ka nui hoihoi ole wale no na mathematicians kahiko a me ka poe akeakamai, akā, no hoi no nā kānaka kuhikuhipuʻuone, pena a me sculptors o nā mea a pau manawa. Ke alo aku o ka wale 5 laha 'me ka loa symmetry polyhedra noʻonoʻo i kekahi kahua Kaka, ka mea, a hiki i hookoia e pili ana me ke kilokilo.

Hexahedron a me kona waiwai

Ma ka palapala o ka hexahedron mau hope Platoʻana i similarity me ka 'ole o ka honua nā'ātoma. O ka papa, e paʻa hōʻoleʻia kāna i kēia kuhiakau, a, naʻe, 'aʻole i ālai ia' aʻe i nā Nails a me ka modernity ia,ʻo ka manaʻo o ka maikaʻi-ikeia na kii o kona mau aesthetics.

I ka anahonua, he hexahedron, oia ka kupa ua noʻonoʻo i ka kūikawā hihia o ka pahu, a, ma ka huli, o keʻano o ka prism. Alaila, na ka waiwai pili i kupa prism waiwai me ka mea wale nō likeʻole i nā mea a pau kihi a me nā kihi o ke kupa i like. Mai keia ke kēia mau waiwai:

1. All kihi o ke kupa i congruent, a moe i ka laua Kekoa me ka pili ana i kekahi i kekahi.
2. All maka - congruent mika pāhoʻonui lua (o ke kupa o 6), kekahi o ka i hiki e ia e like me ke kumu.
3. All pana pua e like intergranal 90.
4. Mai kēlā vertex mai he like ka helu o ka iwiʻaoʻao ona, oia hoi 3.
5. Ke kupa i eiwa o nā koʻi lipi o symmetry, a pau intersect ma ka welau o ke kuʻina o ka diagonals o ka hexahedron, haawiia keia i like me ka waenakonu o ka symmetry.

tetrahedron

Tetrahedron - he tetrahedron me ka lua penei like ma ka shape o triangle mauna, kēlā vertex o i mea no ka huina wahi o ekolu penei.

I ka waiwai o kekahi mau tetrahedron:

1. A pau i ka maka o ka tetrahedron - he equilateral triangle, a 'o ia hoʻi i nā maka a pau o ka tetrahedron i congruent.
2. Mai ke kumu o ke regular geometric huahelu, i mea, e he like aoao, me ka maka o ka tetrahedron a converge ma ka huina like, a laila pau pana pua i like.
3. Huina planar pana pua ma kela a me keia o na vertices mea like i ka 180, no ka mea a pau pana pua i like, i kekahi huina o kekahi papa tetrahedron 60.
4. Kēlā me kēia o nā verticesʻana o kuʻina wahi o na wahi kiekie o ka e ku pono (orthocenter) maka.

Octahedron a me kona waiwai

Hōʻike 'ano o regular polyhedra, ka mea e e kaulana ia mea me he octahedron, i hiki ke visually poe me elua tuko i quadrilateral kumu o mau pyramids.

Nā waiwai o ka octahedron:

1. Ke loa ka inoa o ka geometric kino i kāna ka helu o kona maka. Octahedron haku o ka 8 congruent equilateral triangle mauna, kela mea keia mea o ka i mea like me ka helu ana o vertices nń maka, oia hoi 4.
2. Mai nā maka o ka octahedron e kau like a me kona mau kihi intergranal, kela mea keia mea o i ka 60, a me ka huina o ka planar pana pua kekahi o vertices mea pela 240.

dodecahedron

Inā mākou i manao i na maka a pau o ka geometric kino o ka regular pentagon, e kiʻi i ka dodecahedron - ke aka o 12 polygons.

Waiwai dodecahedron:

1. Ma kēlā me kēia vertex intersect maʻekoluʻaoʻao.
2. All maka i kau like, a i ka like loa o ka iwiʻaoʻao ona, a me ka ewaewa ole wahi.
3. Ma ka dodecahedron 15 koʻi lipi, a Kekoa o symmetry, a me kekahi i kekahi o ia hele ma ka waena o ka luna helehelena, a he alo palena.

icosahedron

Like hana hoihoi ma mua o dodecahedron, icosahedron huahelu ho i ka ekolu-dimensional geometric kino 20 me ka like aoao. Mawaena o na waiwai akau icosahedron nō ke kēia:

1. Nā maka o ka icosahedron - isosceles triangle mauna.
2. Ma kēlā me kēia vertex o ka polyhedron converge elima maka, a me ka huina o ka pili pana pua, he 300 mau poʻo.
3. Icosahedron o ka ia me a me ka dodecahedron, 15 koʻi lipi, a Kekoa o symmetry maalo ae la oia ma na kumu i waenakonu o ke alo aoao.

semiregular polygons

Eia kekahi platonic puaʻa hiwa, polyhedrons convex hui pū nā Archimedean puaʻa hiwa, i mea truncated mau polyhedrons. Ano o ka polyhedra ma keia pae i ke kēia mau waiwai:

1. Geometric kino e pairwise like maka o kekahi mau hoailona ia mea, no ka laʻana, truncated tetrahedron o ka ia me ka regular tetrahedron, 8 maka, akā, i loko o ka hihia kino 4 Archimedean maka i triangular hoʻokino, a 4 - hexagonal.
2. All pana pua i congruent i kekahi vertex.

stellate polyhedra

Poeikohoia? Ueo neobomnyh geometrical kino - stellate polyhedrons, na maka i intersect i kekahi i kekahi. Ka mea hiki ke hana ma kekahi hoʻokuʻi pū o nā regular ekolu-dimensional kino a me ka hopena o ka mau nō lā hoʻi o ko lākou mau maka.

Pela, ua ike stellate polyhedra like: stellate shape o ka octahedron, dodecahedron, icosahedron, cuboctahedral, icosidodecahedron.