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DODECAHEDRON
Mathematics project
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WHAT IS A DODECAHEDRON?
n geometry, a dodecahedron (Greek, from 'twelve' +
'base', 'seat' or 'face') is any polyhedron withtwelve flat faces, but usually a regulardodecahedron is meant: a Platonic solid. It iscomposed of 12 regular pentagonal faces, with
three meeting at each vertex, and is representedby the Schlfli symbol {5,3}. It has 20 vertices and30 edges. Its dual polyhedron is theicosahedrons, with Schlfli symbol {3,5}.
n geometry, a dodecahedron (Greek, from 'twelve' +
'base', 'seat' or 'face') is any polyhedron withtwelve flat faces, but usually a regulardodecahedron is meant: a Platonic solid. It iscomposed of 12 regular pentagonal faces, with
three meeting at each vertex, and is representedby the Schlfli symbol {5,3}. It has 20 vertices and30 edges. Its dual polyhedron is theicosahedrons, with Schlfli symbol {3,5}.
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DODECAHEDRON
The term dodecahedron is also used for other
polyhedra with twelve faces, most notably
the rhombic dodecahedron which is dual tothe cuboctahedron (an Archimedean solid)
and occurs in nature as a crystal form.The
Platonic solid dodecahedron can be called a
pentagonal dodecahedron or a regulardodecahedron to distinguish it.
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A PICTURE SQUE OF
DODECAHEDRONS
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SHAPE OF UNIVERSE
Various models have been proposed for theglobal geometry of the universe. In addition to
the primitive geometries, these proposalsinclude the Poincar dodecahedral space, apositively curved space consisting of adodecahedron whose opposite faces correspond
(with a small twist).T
his was proposed by Jean-Pierre Luminet and colleagues in 2003 and anoptimal orientation on the sky for the model wasestimated in 2008.
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PROPERTIES
If the original dodecahedron has edge length 1, itsdual icosahedron has edge length , the goldenratio.
If we build the five Platonic solids with samevolume, the dodecahedron has the shortestedges.
The map-coloring number of a regular
dodecahedron's faces is 4. The distance between the vertices on the same
face not connected by an edge is .
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IS THE UNIVERSE A
DODECAHEDRON? The standard model of cosmology predicts that
the universe is infinite and flat. However,cosmologists in France and the US are now
suggesting that space could be finite and shapedlike a dodecahedron instead.They claim that auniverse with the same shape as the twelve-sided polygon can explain measurements of the
cosmic microwave background the radiationleft over from the big bang that spaces withmore mundane shapes cannot (J-P Luminet et al.2003 Nature 425 593).
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IS THE UNIVERSE A
DODECAHEDRON?
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DECORATIVE DODECAHEDRONS
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LETS MAKE A DODECAHEDRON
Materials required;
1: colour papers
2: scissor
3: ruler 4: layout of dodecahedron
5: tape
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PROCEDURE
1st: take out and make a rough graph and outline of thedodecahedron with 12 sides in which each sidesangle is 52
2nd
:Score using the straight edge or ruler, as desired.3rd: Cut out the shape so that one piece of paper with
12 pentagons is all that remains.
4th: Fold every printed line segment back andforth. Perhaps pinch the paper between your
thumbnail and forefinger to make the crease or foldvery sharp and more flexible.
5th: Assemble using tape on the inside or outside ofthe solid as desired.
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DODECAHEDRON NETS
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CONGRATULATIONS
Oh! Wow congrats..you have done great
job! Well done. You have prepared a
dodecahedron.look down to see how itlooks.
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GROUP MEMBERS
Dibya debashree dash.
Abhinash samantray.
Partha sarathi rout . Saumyashree nanda.
Sweta dash .
Tejas pattnaik.
