4 / 12 數學精修班 -- a
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4 / 12 數學精修班 -- A. 正多面體面面觀 2. By Fiji. 填寫下列表格. 填寫下列表格. 由表一的數據中,你發現了什麼?. *對偶性質. *都是偶數. *頂點數+面數-邊數=2 即 V + F - E = 2. D. A. C. B. 將正四面體壓扁為平面圖形. 一起來看看正四面體如何壓縮!. D. A. A. C. B. D’. B. 正四面體壓縮. C. 正四面體的射影圖形. A. C. D’. B. 先將線段 AB 拿掉,發現同時 ABD ’ 這個面會消失!. A. C. D’. B. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/1.jpg)
4/12 數學精修班 --A
正多面體面面觀 2
By Fiji
![Page 2: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/2.jpg)
填寫下列表格
正四面體 正六面體 正八面體 正 12面體
正 20 面體
頂點數(V)面數(F)邊數(E)
![Page 3: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/3.jpg)
填寫下列表格
正四面體 正六面體 正八面體 正 12面體
正 20 面體
頂點數(V)
4 8 6 20 12
面數(F)
4 6 8 12 20
邊數(E)
6 12 12 30 30
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正四面體 正六面體 正八面體 正 12面體 正 20面體
頂點數 (V) 4 8 6 20 12
面數 (F) 4 6 8 12 20
邊數 (E) 6 12 12 30 30
由表一的數據中,你發現了什麼?
*都是偶數 *對偶性質
*頂點數+面數-邊數=2
即 VV ++ FF -- EE ==22
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將正四面體壓扁為平面圖形
一起來看看正四面體如何壓縮!
A
B
C
D
![Page 6: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/6.jpg)
正四面體壓縮
A
B
CD’
CA
B
D
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正四面體的射影圖形
A
B
C
D’
![Page 8: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/8.jpg)
先將線段 AB拿掉,發現同時 ABD’這個面會消失!
A
B
C
D’
![Page 9: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/9.jpg)
分別拿掉線段 BC、線段 AC,發現面BCD’、面 ACD’會消失!
A
B
C
D’
![Page 10: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/10.jpg)
A
B
C
D’
分別拿掉線段 BC、線段 AC,發現面BCD’、面 ACD’會消失!
![Page 11: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/11.jpg)
拿掉頂點 A,發現少了邊 AD’
A
B
C
D’
![Page 12: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/12.jpg)
A
B
C
D’
拿掉頂點 B、 C,發現少了邊 BD’、CD’
![Page 13: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/13.jpg)
A
B
C
D’
拿掉頂點 B、 C,發現少了邊 BD’、CD’
最後剩下一個頂點 D’,即證明
V’ + F’ – E’ = 1
![Page 14: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/14.jpg)
正六面體的射影圖形
看看正六面體如何壓縮!
![Page 15: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/15.jpg)
正六面體壓縮
![Page 16: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/16.jpg)
正六面體的射影圖形
![Page 17: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/17.jpg)
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正八面體的射影圖形
A
B
C
D
E
F
看看正八面體如何壓縮!
![Page 30: 4 / 12 數學精修班 -- A](https://reader035.vdocuments.net/reader035/viewer/2022081420/5681313b550346895d97b1f2/html5/thumbnails/30.jpg)
正八面體壓縮
B
A C
D'
F'
E'
A
B
C
D
E
F
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正 12面體和正 20面體又如何壓縮呢?
D
E
FG
H
I
J
K
LA
BC
M
N
O
P
Q
R S
T
A
B
C
D E
FG
H
J
KL
I
大家來挑戰!!!
大家來挑戰!!!