FUUASTDept. of Com. Sc. & IT1 Computer Graphics Prof. Muhammad Saeed Department of Computer Science & IT Federal Urdu University of Arts, Science and Technology.

FUUAST Dept. of Com. Sc. & IT 1

Computer GraphicsComputer GraphicsComputer GraphicsComputer GraphicsProf. Muhammad Saeed

Department of Computer Science & IT Federal Urdu University of Arts, Science and Technology

FUUAST Dept. of Com. Sc. & IT 2

Computer Graphics

Platonic Solids

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Computer Graphics

Hexahedron(Cube)

Vertices Faces Edges

8 6 12

FUUAST Dept. of Com. Sc. & IT 4

Computer Graphics

float [,] cube = { { 0.5, 0.5, 0.5 }, { 0.5, 0.5, -0.5 }, { -0.5, 0.5, -0.5 }, { -0.5, 0.5, 0.5 }, { 0.5, -0.5, 0.5 }, { 0.5, -0.5, -0.5 }, { -0.5, -0.5, -0.5 }, { -0.5, -0.5, 0.5 } };int [,] cubeEdges = { {0,1},{1,2},{2,3},{3,0}, {4,5},{5,6},{6,7},{7,4}, {0,4},{1,5},{2,6},{3,7} };

int [,] cubeFaces={{0,1,2,3},{4,5,6,7},{0,4,5,1},{3,2,6,7},{0,3,7,4},{2,1,5,6}};

Vertices, Edges and Faces of Cube (Centered at Origin)

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Computer Graphics

Tetrahedron

Vertices Faces Edges

4 4 6

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Computer Graphics

float[,] tetra = { { -0.5, -0.288675133647, -0.20412414525 }, { 0.5, -0.288675133647 -0.20412414525}, { 0.0, 0.577350266353, -0.20412414525}, { 0.0, 0.0, 0.61237243575} }; int[,] tetraEdges={ {0,1},{1,2},{2,0}, {0,3},{1,3},{2,3} };

int[,] tetraFaces = { {0,2,1 },{0,1,3},{1,2,3},{0,3,2}};

Vertices, Edges and Faces of Tetrahedron (Centered at Origin)

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Computer Graphics

Octahedron

Vertices Faces Edges

6 8 12

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Computer Graphics

float[,] octa = { {-0.5, -0.5, 0, }, { 0.5, -0.5, 0, }, { 0.5, 0.5, 0, }, {-0.5, 0.5, 0, }, { 0, 0, 0.70710678 }, { 0, 0, -0.70710678 } };int[,] octaEdges ={ {0,1},{1,2},{2,3},{3,0}, {0,4},{1,4},{2,4},{3,4}, {0,5},{1,5},{2,5},{3,5} };int[,] octaFaces = { {0,1,4},{1,2,4},{2,3,4},{3,0,4}, {0,5,1},{5,2,1},{5,3,2},{0,3,5} };

Vertices, Edges and Faces of Octahedron (Centered at Origin)

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Computer Graphics

Icosahedron

Vertices Faces Edges

12 20 30

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Computer Graphics

float[,] icosa = { {-0.5, -0.68819096, 0.425325404 }, { 0.5, -0.68819096, 0.425325404 }, {0.809016995, 0.262865559, 0.425325404 }, {0.0, 0.850650808, 0.425325404 }, {-0.809016995, 0.262865559, 0.425325404 }, {0, -0.850650808, -0.425325404 }, {0.809016995, -0.262865557, -0.425325404 }, {0.5, 0.68819096, -0.425325404 }, {-0.5, 0.68819096, -0.425325404 }, {-0.809016995, -0.262865551, -0.425325404 }, {0, 0, 0.951056516 }, {0, 0, -0.951056516 } };

Vertices, Edges and Faces of Icosahedron (Centered at Origin)

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Computer Graphics

int [,] icosaEdges = { {0,1},{1,2},{2,3},{3,4},{4,0}, {5,6},{6,7},{7,8},{8,9},{9,5}, {0,5},{5,1},{1,6},{6,2},{2,7},{7,3},{3,8},{8,4},{4,9},{9,0}, {0,10},{1,10},{2,10},{3,10},{4,10}, {5,11},{6,11},{7,11},{8,11},{9,11}

};

int [,] icosaFaces = { {0,1,10},{1,2,10},{2,3,10},{3,4,10},{4,0,10}, {6,5,11},{7,6,11},{8,7,11},{9,8,11},{5,9,11}, {1,0,5},{1,5,6},{2,1,6},{2,6,7},{3,2,7}, {3,7,8},{4,3,8},{4,8,9},{0,4,9},{0,9,5} };

Vertices, Edges and Faces of Icosahedron (Centered at Origin)

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Computer Graphics

Dodecahedron

Vertices Faces Edges

20 12 30

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Computer Graphics

float[,] dodeca = { 0, -0.458793974, 0.600569108 }, {0.436338997, -0.141775134, 0.600569108 }, {0.26967233, 0.371172122, 0.600569108 }, {-0.26967233, 0.371172122, 0.600569108 }, {-0.436338997, -0.141775134, 0.600569108 }, {0.269672331, -0.371172123, -0.600569108 }, {0.436338997, 0.141775134, -0.600569108 }, {0, 0.458793973, -0.600569108 }, {-0.436338997, 0.141775134, -0.600569108 }, {-0.269672331, -0.371172123, -0.600569108 },

{0, -0.742344244, 0.141775134 }, {0.436338997, -0.60056911, -0.141775134 }, {0.706011328, -0.229396987, 0.141775134 }, {0.706011328, 0.229396987, -0.141775134 }, {0.436338997, 0.600569109, 0.141775134 },

Vertices, Edges and Faces of Dodecahedron (Centered at Origin)

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Computer Graphics

{0, 0.742344243, -0.141775134 }, {-0.436338997, 0.600569108, 0.141775134 }, {-0.706011328, 0.229396987, -0.141775134 }, {-0.706011328, -0.229396987, 0.141775134 }, {-0.436338997, -0.600569108, -0.141775134 } };

Continued …………

int [,] dodecaEdges = { {0,1},{1,2},{2,3},{3,4},{4,0}, {5,6},{6,7},{7,8},{8,9},{9,5}, {0,10},{1,12},{2,14},{3,16},{4,18}, {10,11},{11,12},{12,13},{13,14},{14,15},{15,16},{16,17},{17,18},{18,19},{19,10}, {5,11},{6,13},{7,15},{8,17},{9,19} };

int [,] dodecaFaces = { { 4,3,2,1,0}, {5,6,7,8,9}, {12,11,10,0,1}, {1,2,14,13,12}, {2,3,16,15,14}, {3,4,18,17,16}, {0,10,19,18,4}, {11,12,13,6,5}, {13,14,15,7,6}, {7,8,17,16,15}, {9,8,17,18,19}, {10,11,5,9,19}

};

Vertices, Edges and Faces of Dodecahedron (Centered at Origin)

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Computer Graphics

Non Platonic Archimedian Buckyball (Truncated Icosahedron)Vertices Faces Edges

60 32 90

Consists of 20 Regular Hexagons & 12 Regular Pentagons

Has many types and number of faces differ from type to typeData ( Vertices and Edges) in separate file

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Computer Graphics

Buckyball consists of 20 regular hexagons & 12 regular pentagons

has many types and number of faces differ from type to type

Data for all the solids discussed include1)Vertices2)Edges3)Faces(Surfaces)4)Normals(unit)

Filename: DataForPlatonicSolidsBuckyball.doc

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Computer Graphics

ENDPlatonic Solids