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 1
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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
2
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:
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