3 d polyhedral

8/3/2019 3 D Polyhedral

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1"L _gd}ciluhd



Xyiq|mgk 8

Pch| mq pdh|gkma qgdml7



LIFMKM\MGK

_dh|gkma qgdml mq h agkvis pgd}cilugk|ch| mq ui`ydhu$ mk |ci qikqi gf h ui`ydhupgd}`gk+



\]_IQ

\ciui hui puiamqid} fmvi |}piq gf _dh|gkma qgdmlq:

ayei lgliahcilugk magqhcilugk ga|hcilugk |i|uhcilugk



_UG_IU\MIQ

8+H agkvis pgd}cilugk mq h _dh|gkma qgdmlmf hkl gkd} mf

‥hdd m|q fhaiq hui agk`uyik| agkvisui`ydhu pgd}`gkq$‥kgki gf m|q fhaiq mk|iuqia| isaip| h| |cimu

il`iq$ hkl‥|ci qhbi kybeiu gf fhaiq bii| h| ihacgf m|q viu|maiq



5+Ihac _dh|gkma qgdml ahk |ciuifgui eilikg|il e} h q}begd ~p $ x r ciui

p 2 |ci kybeiu gf il`iq gf ihac fhai #gu |cikybeiu gf viu|maiq gf ihac fhai- hklx 2 |ci kybeiu gf fhaiq bii|mk` h| ihacviu|is #gu |ci kybeiu gf il`iq bii|mk` h|ihac viu|is-+

_UG_IU\MIQ



1+\ci q}begd ~p $ x r$ ahddil |ci Qacdìfdm

q}begd$ `mviq h agbemkh|gumhdliqaump|mgk gf |ci pgd}cilugk+ \ciQacdìfdm q}begdq gf |ci fmvi _dh|gkmaqgdmlq hui `mvik mk |ci |hedi eidg+

_UG_IU\MIQ



H agbemkh|gumhd liqaump|mgk gf |ci

pgd}cilugk

_gd}cilugk Viu|maiq Il`iq FhaiqQacdìfdm

q}begd

Viu|is

agkfm`yuh|mgk

\i|uhcilugk < 6 < ~1$ 1r 1+1+1

Ayei 3 85 6 ~<$ 1r <+<+<

Ga|hcilugk 6 85 3 ~1$ <r 1+1+1+1

Lgliahcilugk 5? 1? 85 ~9$ 1r 9+9+9

Magqhcilugk 85 1? 5? ~1$ 9r 1+1+1+1+1



Pch| mq Huacmbilihk qgdml7

Xyiq|mgk 5



LIFMKM\MGK

‥Mk `igbi|u} hk Huacmbilihk qgdml mqh cm`cd} q}bbi|uma$ qibm"ui`ydhuagkvis pgd}cilugk agbpgqil gf |g gubgui |}piq gf ui`ydhu pgd}`gkq bii|mk`

mk mlik|mahd viu|maiq+



ADHQQMFMAH\MGK

\ciui hui 81 Huacmbilihk qgdmlq #89 mf |cibmuugu mbh`iq gf |g ikhk|mgbgupcq-

Ciui |ci viu|is agkfm`yuh|mgk uifiuq |g |ci|}pi gf ui`ydhu pgd}`gkq |ch| bii| h| hk}`mvik viu|is+ Fgu ishbpdi$ h viu|isagkfm`yuh|mgk gf #<$6$3- bihkq |ch| h qxyhui$

cish`gk$ hkl ga|h`gk bii| h| h viu|is #m|c|ci guliu |hnik |g ei adganmqi hugykl |civiu|is-+



_UG_IU\MIQ

‥\ci kybeiu gf viu|maiq mq 05?¿ lmvmlil e} |civiu|is hk`di lifia|+

‥\ci ayega|hcilugk hkl magqmlgliahcilugk huiil`i"ykmfgub hkl hui ahddil xyhqm"ui`ydhu+

‥\ci lyhdq gf |ci Huacmbilihk qgdmlq hui ahddil|ci Ah|hdhk qgdmlq+ \g`i|ciu m|c |ci emp}uhbmlq

hkl |uhpizgciluh$ |ciqi hui |ci fhai"ykmfgubqgdmlq m|c ui`ydhu viu|maiq+



Khbi

#Viu|is

agkfm`yuh|mgk-


qkye ayeigu qkye

cishcilugk

gu qkye

ayega|hcilugk

#5 acmuhd fgubq-

#1+1+1+1+<-

13 15

|umhk`diq

6 qxyhuiq 6? 5<

magqmlgliahci

lugk

#1+9+1+9- 15

5?

|umhk`diq

85

pik|h`gkq

6? 1?

|uykah|il

lgliahcilugk

#1+8?+8?- 15

5?

|umhk`diq

85

liah`gkq

=? 6?

http://en.wikipedia.org/wiki/File:Truncated_dodecahedron.png

http://en.wikipedia.org/wiki/File:Icosidodecahedron.png

http://en.wikipedia.org/wiki/File:Snub_hexahedron.png



Khbi

#Viu|is

agkfm`yuh|mgk-


|uykah|ilmagqhcilugk

gu eyan}ehdd

gu fgg|ehdd'qgaaiu

ehdd

#9+6+6 -

15

85

pik|h`gkq

5?

cish`gkq

=? 6?

ucgbemagqmlgliahcilugk

gu qbhdd

ucgbemagqmlgliahci

lugk

#1+<+9+<-

65

5?

|umhk`diq

1? qxyhuiq

85

pik|h`gkq

85? 6?

|uykah|ilmagqmlgliahcilugk

gu `uih|

ucgbemagqmlgliahci

lugk

#<+6+8?-

65

1? qxyhuiq

5?

cish`gkq

85

liah`gkq

83? 85?



Khbi

#Viu|is

agkfm`yuh|mgk-


qkye

lgliahcilugkgu qkye

magqmlgliahci

lugk

#5 acmuhd

fgubq-

#1+1+1+1+9-

=5

3? |umhk`diq

85

pik|h`gkq

89? 6?



Xyiq|mgk 1

Lmqayqq gul vgaheydhu}dhk`yh`i |g liqaumei 5L qchpi

hkl 1L qgdml +



VGAHEYDHU] QIQMGK

5"L Qchpi

Amuadi$ qxyhui$ |umhk`di$ ayuvi$ qibm"amuadi + + + +

1"L Qchpi

Qpciui$ ayei$ pumqb$ ayegmlq + + + +

Ahk }gy |cmkn g|ciuq vgaheydhu} mkq|ihl gf

|ciqi7



Xyiq|mgk <

Pc} acmdluik qcgydl dihuk`igbi|u}7



Uihqgk 5

Dg`mahd |cmknmk`: Lgmk` puggfq uixymuiqdg`mahd |cmknmk`$ h bik|hd pugaiqq |ch| mq

uhuid} idd lividgpil mk |ci }gyk`iu cm`cqacggd q|ylik|q+ \ci ha| gf lgmk` puggfqpugvmliq q|ylik|q m|c h `uih| gppgu|ykm|} |glividgp$ gu mbpugvi ypgk$ |cmq vhdyhedi

cm`ciu guliu |cmknmk` pugaiqq+



\ch|”q hdd+ +

3 d polyhedral

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