Bahagian 2

Dalam kumpulan dua orang, anda dikehendaki membina model yang terdiri

daripada dua jenis polyhedral.

Polyhedron

The word polyhedron has slightly different meanings in geometry and

algebraic geometry. In geometry, a polyhedron is simply a three-dimensional

solid which consists of a collection of polygons, usually joined at their edges.

The word derives from the Greek poly (many) plus the Indo-European hedron

(seat). A polyhedron is the three-dimensional version of the more general

polytope (in the geometric sense), which can be defined in arbitrary

dimension. The plural of polyhedron is "polyhedra" (or sometimes

"polyhedrons").

The term "polyhedron" is used somewhat differently in algebraic topology,

where it is defined as a space that can be built from such "building blocks" as

line segments, triangles, tetrahedra, and their higher dimensional analogs by

"gluing them together" along their faces (Munkres 1993, p. 2). More

specifically, it can be defined as the underlying space of a simplicial complex

(with the additional constraint sometimes imposed that the complex be finite;

Munkres 1993, p. 9). In the usual definition, a polyhedron can be viewed as

an intersection of half-spaces, while a polytope is a bounded polyhedron.

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A convex polyhedron can be formally defined as the set of solutions to a

system of linear inequalities

where is a real matrix and is a real -vector. Although usage varies,

most authors additionally require that a solution be bounded for it to define a

convex polyhedron. An example of a convex polyhedron is illustrated above.

The following table lists the name given to a polyhedron having faces for

small . When used without qualification for polyhedron for which symmetric

forms exist, the term may mean this particular polyhedron or may mean a

arbitrary -faced polyhedron, depending on context.

polyhedron

4 tetrahedron

5 pentahedron

6 hexahedron

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7 heptahedron

8 octahedron

9 nonahedron

1

0decahedron

1

1undecahedron

1

2dodecahedron

1

4tetradecahedron

2

0icosahedron

2

4icositetrahedron

3

0triacontahedron

3

2icosidodecahedron

6

0hexecontahedron

9

0enneacontahedron

A polyhedron is said to be regular if its faces and vertex figures are regular

(not necessarily convex) polygons (Coxeter 1973, p. 16). Using this definition,

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there are a total of nine regular polyhedra, five being the convex Platonic

solids and four being the concave (stellated) Kepler-Poinsot solids. However,

the term "regular polyhedra" is sometimes used to refer exclusively to the

Platonic solids (Cromwell 1997, p. 53). The dual polyhedra of the Platonic

solids are not new polyhedra, but are themselves Platonic solids.

A convex polyhedron is called semiregular if its faces have a similar

arrangement of nonintersecting regular planar convex polygons of two or

more different types about each polyhedron vertex (Holden 1991, p. 41).

These solids are more commonly called the Archimedean solids, and there

are 13 of them. The dual polyhedra of the Archimedean solids are 13 new

(and beautiful) solids, sometimes called the Catalan solids.

A quasiregular polyhedron is the solid region interior to two dual regular

polyhedra (Coxeter 1973, pp. 17-20). There are only two convex quasiregular

polyhedra: the cuboctahedron and icosidodecahedron. There are also infinite

families of prisms and antiprisms.

There exist exactly 92 convex polyhedra with regular polygonal faces (and not

necessarily equivalent vertices). They are known as the Johnson solids.

Polyhedra with identical polyhedron vertices related by a symmetry operation

are known as uniform polyhedra. There are 75 such polyhedra in which only

two faces may meet at an polyhedron edge, and 76 in which any even

number of faces may meet. Of these, 37 were discovered by Badoureau in

1881 and 12 by Coxeter and Miller ca. 1930.

Polyhedra can be superposed on each other (with the sides allowed to pass

through each other) to yield additional polyhedron compounds. Those made

from regular polyhedra have symmetries which are especially aesthetically

pleasing. The graphs corresponding to polyhedra skeletons are called

Schlegel graphs.

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SAMPEL POLYHEDRAL1.

FIG.3 - The truncated icosido-decahedron (on the left) and the rhombic icosi-dodecahedron

(on the right) are a couple of Archimedean polyhedra generated from the intersection of three

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polyhedra: an icosahedron, a dodecahedron and a rhombic triacontahedron. When the ratios

between the distances of their faces from the centre of the resulting polyhedron get

appropriate values, the faces are regular polygons: together with squares, in the first case

there are decagons and hexagons that, in the second case, become pentagons and triangles,

respectively.

2. Model Polyhedral

3.MODEL POLYHEDRAL

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4.MODEL POLYHEDRAL

5. MODEL POLYHEDRAL

6. MODEL POLYHEDRAL

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6. MODEL POLYHEDRAL

POLYHEDRAL YANG DIBUAT OLEH KUMPULAN KAMI IALAH GABUNGAN PIRAMID DAN KUBUS

LANGKAH-LANGKAH MEMBUAT:

Langkah 1: Menyediakan kertas berbentuk segiempat dan membuta libatan

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Sambunagan daripada lipatan di atas

Langkah 2 : Membuat 5 lipatan yang sama pada kertas warna yang lain.

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Langkah 3 : Cantumkan keenam-enam lipatan tersebut untuk menjadi polyhedral yang berwarna-warni

REFLEKSI:

Pertama sekali, kami ingin mengucapkan ribuan terima kasih kepada

pensyarah En. Chiong untuk mengarahkan tajuk polyhedral ini untuk kami.

Kami berasa bangga juga kerana berpeluang lagi bekerjasama untuk

menyiapkan kerja kursus kami selepas 6 tahun. Semasa kami menerima

soalan ini, En. Chiong telah menunjukkan kami satu model polyhedral yang

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mudah untuk dirujuk kami. Kami memang tiada idea pada masa itu. Selepas

kami membuat perbingcangan, kami telah membahagikan tugas kami untuk

mencari bahan dan maklumat daripada pelbagai sumber. Kami juga menanya

kepada kawan-kawan yang pandai membuat polyhedral. Banyak maklumat

yang kamicarikan daripada internet.

Masalah yang kami hadapi untuk membuat polyhedral ini ialah kami

bukan dari satu tempat menyebabkan kami susah untuk berkomunikasi

antara satu sama lain. Nasib baik terdapat satu cuti satu minggu pada bulan

Ogos. Kami telah membuat perbincangan pada masa itu. Maklumat yang

kami carikan kebanyakannya bahasa inggeris kerana jarang dalam bahasa

Malaysia. Kami telah membuat pengagihan untuk menyiapkan tugasan. Kami

banyak mempelajari daripada proses membuat polyhedral dan telah

mengenali pelbagai polyhedral. Kami berharap tugasan ini berguna untuk

kami pada masa yang akan datang.

BIBLIOGRAFI

Rujukan daripada laman web:

1. http://mathworld.wolfram.com/Polyhedron.html

2. http://flickrhivemind.net/Tags/polyhedron

3. www.boxvox.net/2008/05/polyhedral-mode.html

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4. www.mi.sanu.ac.rs/vismath/zefirocorrection/__Zefiro-

Ardigo'_icosahedral_polyhedra_updating.htm

5. http://numb3rs.wolfram.com/406/

6. http://www.platonicsolids.info/origami.htm TEACHING

7. http://www.maa.org/mathland/mathtrek_04_23_06.html

8. http://en.wikipedia.org/wiki/File:Uniform_polyhedron-53-s012.png

9. http://www.123rf.com/photo_6761776_polyhedral-figure-of-a-star-with-

gradient-vector-3d.html

VIDEO:

1. http://www.youtube.com/watch?v=2Yp3w2Dy3C8&feature=relmfu

2. http://www.youtube.com/watch?v=P9yLyT9C5bA&feature=related

3. http://www.youtube.com/watch?v=8Kr0Og_HR7Q&feature=relmfu

4. http://www.youtube.com/watch?v=aa2oxlxwFUY&feature=related

5. http://www.youtube.com/watch?v=ov7xwi_nhBc&feature=related

6. http://www.youtube.com/watch?v=n2SsCzf1no0&feature=related

7. http://www.youtube.com/watch?v=H7qE_Tc8e4g&feature=related

Borang Rekod Kolaborasi Kerja Kursus

NAMA PELAJAR : TIONG ING CHIONG / HII ING YEU

NO. MATRIK KP : 830601-13-5545 / 840927-13-5624

KUMPULAN : PPG PJK AMBILAN JUN 2011

MATA PELAJARAN : WAJ3105 LITERASI NOMBOR

PENSYARAH PEMBIMBING : EN. CHIONG YEW KAI

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Tarikh Aktiviti yang dijalankan Nama /Tandatangan

2.7.2011 Menerima soalan tugasan daripada

pensyarah.

Penerangan daripada pensyarah.

TIONG ING CHIONG

HII ING YEU

15.7.2011 Membahagikan tugas

Mencari maklumat dari

internet/perpustakaan awam.

TIONG ING CHIONG

HII ING YEU

27.8.2011 Berbincang bersama untuk

meneyelesaikan maslah yang dihadapi. TIONG ING CHIONG

HII ING YEU

16.9.2011 Membuat polyhedral

Menaip semua bahan dan maklumat.

Menyemak tugasan

TIONG ING CHIONG

HII ING YEU

24.9.2011 Menghantar hasil tugasan yang telah

disiapkan kepada pensyarah pembimbing. TIONG ING CHIONG

HII ING YEU

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