Geometry Worksheet -- Nets of Platonic and Archimedean Solids

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Geometry Worksheet -- Nets of Platonic and Archimedean Solids

Net of a Tetrahedron Cut out. Fold along lines. Tape or glue tabs. Tetrahedron Math-Drills.com Net of a Cube Cut out. Fold along lines. Tape or glue tabs. Cube Math-Drills.com Net of an Octahedron Cut out. Fold along lines. Tape or glue tabs. Octahedron Math-Drills.com Net of a Dodecahedron 1 Cut out. Fold along lines. Tape or glue tabs. Dodecahedron Math-Drills.com Net of a Dodecahedron 2 Cut out. Fold along lines. Tape or glue tabs. Dodecahedron Math-Drills.com Net of an Icosahedron Cut out. Fold along lines. Tape or glue tabs. Icosahedron Math-Drills.com Net of a Truncated Tetrahedron Cut out. Fold along lines. Tape or glue tabs. Truncated Tetrahedron Math-Drills.com Net of a Cuboctahedron Cut out. Fold along lines. Tape or glue tabs. Cuboctahedron Math-Drills.com Net of a Truncated Cube Cut out. Fold along lines. Tape or glue tabs. Truncated Cube Math-Drills.com Net of a Truncated Octahedron Cut out. Fold along lines. Tape or glue tabs. Truncated Octahedron Math-Drills.com Net of a Rhombicuboctahedron Cut out. Fold along lines. Tape or glue tabs. Rhombi- cuboctahedron Math-Drills.com Net of a Truncated Cuboctahedron Cut out. Fold along lines. Tape or glue tabs. Truncated Cuboctahedron Math-Drills.com Net of a Snub Cube Cut out. Fold along lines. Tape or glue tabs. Snub Cube Math-Drills.com Net of an Icosidodecahedron Cut out. Fold along lines. Tape or glue tabs. Icosidodecahedron Math-Drills.com.

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On the Archimedean Or Semiregular Polyhedra
ON THE ARCHIMEDEAN OR SEMIREGULAR POLYHEDRA Mark B. Villarino Depto. de Matemática, Universidad de Costa Rica, 2060 San José, Costa Rica May 11, 2005 Abstract We prove that there are thirteen Archimedean/semiregular polyhedra by using Euler’s polyhedral formula. Contents 1 Introduction 2 1.1 RegularPolyhedra .............................. 2 1.2 Archimedean/semiregular polyhedra . ..... 2 2 Proof techniques 3 2.1 Euclid’s proof for regular polyhedra . ..... 3 2.2 Euler’s polyhedral formula for regular polyhedra . ......... 4 2.3 ProofsofArchimedes’theorem. .. 4 3 Three lemmas 5 3.1 Lemma1.................................... 5 3.2 Lemma2.................................... 6 3.3 Lemma3.................................... 7 4 Topological Proof of Archimedes’ theorem 8 arXiv:math/0505488v1 [math.GT] 24 May 2005 4.1 Case1: fivefacesmeetatavertex: r=5. .. 8 4.1.1 At least one face is a triangle: p1 =3................ 8 4.1.2 All faces have at least four sides: p1 > 4 .............. 9 4.2 Case2: fourfacesmeetatavertex: r=4 . .. 10 4.2.1 At least one face is a triangle: p1 =3................ 10 4.2.2 All faces have at least four sides: p1 > 4 .............. 11 4.3 Case3: threefacesmeetatavertes: r=3 . ... 11 4.3.1 At least one face is a triangle: p1 =3................ 11 4.3.2 All faces have at least four sides and one exactly four sides: p1 =4 6 p2 6 p3. 12 4.3.3 All faces have at least five sides and one exactly five sides: p1 =5 6 p2 6 p3 13 1 5 Summary of our results 13 6 Final remarks 14 1 Introduction 1.1 Regular Polyhedra A polyhedron may be intuitively conceived as a “solid figure” bounded by plane faces and straight line edges so arranged that every edge joins exactly two (no more, no less) vertices and is a common side of two faces.
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Archimedean Solids
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