Fișier:Full octahedral group elements in truncated cuboctahedron; JF.png

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Descriere fișier

Descriere

Elements of the full octahedral group as permutations of identified with vertices of the truncated cuboctahedron

The neutral element is the light JF on the left. The light vertices are its 24 rotations. The dark ones are reflections.

Această imagine a fost creată cu Persistence of Vision.

Dată

25 februarie 2018

Sursă

Operă proprie

Autor

Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

Licențiere

Eu, deținătorul drepturilor de autor ale acestei opere, prin prezenta îmi public lucrarea sub următoarele licențe:

Se permite copierea, distribuirea și/sau modificarea acestui document conform termenilor Documentației de licență liberă GNU, versiunea 1.2 sau orice altă versiune ulterioară publicată de Free Software Foundation, fără părți neschimbabile, texte de pe copertele principale și finale. O copie a acestei licențe este inclusă în secțiunea numită Documentația de licență liberă GNU.

Acest fișier a fost eliberat sub licența Creative Commons Atribuire 4.0 Internațională.

Sunteți liber:

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POV-Ray source

#version 3.6;
global_settings { assumed_gamma 1.0 }
#default{ finish{ ambient 0.1 diffuse 0.9 conserve_energy}}

#include "colors.inc"
#include "math.inc"
#include "textures.inc"


///////////////////////////// camera and light

#declare Camera_Position = <13.2, 10.5, -45>;
camera{
    location Camera_Position
    right    x*image_width/image_height
    angle    10.45
    look_at  <0, 0, 0>
}

light_source{ <-400, 500, -300> color White*0.9 shadowless}
light_source{ <400, 200, 100> color White*0.4 shadowless}
light_source{ Camera_Position  color rgb<0.9,0.9,1>*0.2 shadowless}
sky_sphere{ pigment{ White } }

///////////////////////////// sizes

#declare RadVert = .04;
#declare RadEdge = .01;

///////////////////////////// colors

#declare DarkColor = rgb<0.005, 0.004, 0.004>;  // edges of the JF compound

#declare Darkbrown = rgb<1,0.8,0.65>*.2;
#declare Lightbrown = rgb<1,0.8,0.65>*.5;

#declare EdgeColor = DarkColor;  // polyhedron
#declare FaceColor = rgbt <1, 1, 1, .7>;  // polyhedron


///////////////////////////////////////////////// macro to create the JF compound in the provided color

#macro letterJF(LightColor)

    #declare BigCyl = cylinder{ <0, 0, 0>, <0.9, 0, 0>, 1.5 }
    #declare SmallCyl = cylinder{ <-0.1, 0, 0>, <1, 0, 0>, 0.6 }
    #declare Ring = difference{
        object{BigCyl}
        object{SmallCyl}
    }
    #declare CutBox = box{
        <-10,-10,-10> <10,10,10>
        translate 10*y
    }
    #declare HalfRing = difference{
        object{Ring}
        object{CutBox}
    }
    #declare CutBox = object{
        CutBox
        rotate -45*x
        pigment{color DarkColor}
    }
    #declare LetterJTail = difference{
        object{HalfRing}
        object{CutBox}
    }


    #declare LetterStem = box{
        <0, 0, 0.6>
        <0.9, 2.4, 1.5>
    }


    #declare LetterFBar1 = box{
        <0, 1.5, 0.6>
        <-3, 2.4, 1.5>
    }
    #declare CutBox = box{
        <-10,-10,-10> <10,10,10>
        translate <-12.6, 0, 0>
        pigment{color DarkColor}
    }
    #declare LetterFBar1 = difference{
        object{LetterFBar1}
        CutBox
    }


    #declare LetterFBar2 = object{
        LetterFBar1
        translate <0, -1.5, 0>
    }
    #declare CutBox = object{
        CutBox
        translate <1.3, 0, 0>
    }
    #declare LetterFBar2 = difference{
        object{LetterFBar2}
        CutBox
    }


    #declare LetterJFSolid = union{
        object{LetterJTail}
        object{LetterStem}
        object{LetterFBar1}
        object{LetterFBar2}
        pigment{color LightColor}
    }


    ///////////////////////////// JF outline

    #declare R = 0.03;

    #declare PointFBar1a = <0.9, 2.4, 0.6>;
    #declare PointFBar1b = PointFBar1a + 0.9*z;
    #declare PointFBar1c = PointFBar1a - 3.5*x;
    #declare PointFBar1d = PointFBar1b - 3.5*x;

    #declare PointFBar2c = PointFBar1c - 0.9*y;
    #declare PointFBar2d = PointFBar2c + 0.9*z;
    #declare PointFBar2a = PointFBar2c + 2.6*x;
    #declare PointFBar2b = PointFBar2a + 0.9*z;

    #declare PointFBar3a = PointFBar2a - 0.6*y;
    #declare PointFBar3b = PointFBar3a + 0.9*z;
    #declare PointFBar3c = PointFBar3a - 1.3*x;
    #declare PointFBar3d = PointFBar3b - 1.3*x;

    #declare PointFBar4a = PointFBar3a - 0.9*y;
    #declare PointFBar4b = PointFBar4a + 0.9*z;
    #declare PointFBar4c = PointFBar4a - 1.3*x;
    #declare PointFBar4d = PointFBar4b - 1.3*x;

    #declare PointJFaceA = PointFBar4a + 0.9*x;
    #declare PointJFaceB = PointFBar4b + 0.9*x;

    #declare PointJEndA = <0.9, -sqrt(1.125), -sqrt(1.125)>;
    #declare PointJEndB = <0.9, -sqrt(0.18), -sqrt(0.18)>;
    #declare PointJEndC = PointJEndA - 0.9*x;
    #declare PointJEndD = PointJEndB - 0.9*x;


    #declare SmallTorus = object{
        torus {0.6, R}
        rotate 90*z
    }
    #declare BigTorus = object{
        torus {1.5, R}
        rotate 90*z
    }
    #declare Tori1 = union{
        object{SmallTorus}
        object{BigTorus}
    }
    #declare Tori2 = object{
        Tori1
        translate 0.9*x
    }
    #declare Tori = union{
        object{Tori1}
        object{Tori2}
    }

    #declare CutBox = box{
        <-10,-10,-10> <10,10,10>
        translate 10*y
    }
    #declare Tori = difference{
        object{Tori}
        object{CutBox}
    }
    #declare CutBox = object{
        CutBox
        rotate -45*x
    }
    #declare Tori = difference{
        object{Tori}
        object{CutBox}
    }


    #declare LetterJFOutlines = union{

        sphere{PointFBar1a, R}
        sphere{PointFBar1b, R}
        sphere{PointFBar1c, R}
        sphere{PointFBar1d, R}

        sphere{PointFBar2a, R}
        sphere{PointFBar2b, R}
        sphere{PointFBar2c, R}
        sphere{PointFBar2d, R}

        sphere{PointFBar3a, R}
        sphere{PointFBar3b, R}
        sphere{PointFBar3c, R}
        sphere{PointFBar3d, R}

        sphere{PointFBar4a, R}
        sphere{PointFBar4b, R}
        sphere{PointFBar4c, R}
        sphere{PointFBar4d, R}

        sphere{PointJEndA, R}
        sphere{PointJEndB, R}
        sphere{PointJEndC, R}
        sphere{PointJEndD, R}

        cylinder{PointFBar1a, PointFBar1b, R}
        cylinder{PointFBar1b, PointFBar1d, R}
        cylinder{PointFBar1d, PointFBar1c, R}
        cylinder{PointFBar1c, PointFBar1a, R}

        cylinder{PointFBar2a, PointFBar2b, R}
        cylinder{PointFBar2b, PointFBar2d, R}
        cylinder{PointFBar2d, PointFBar2c, R}
        cylinder{PointFBar2c, PointFBar2a, R}

        cylinder{PointFBar3a, PointFBar3b, R}
        cylinder{PointFBar3b, PointFBar3d, R}
        cylinder{PointFBar3d, PointFBar3c, R}
        cylinder{PointFBar3c, PointFBar3a, R}

        cylinder{PointFBar4a, PointFBar4b, R}
        cylinder{PointFBar4b, PointFBar4d, R}
        cylinder{PointFBar4d, PointFBar4c, R}
        cylinder{PointFBar4c, PointFBar4a, R}

        cylinder{PointFBar1c, PointFBar2c, R}
        cylinder{PointFBar1d, PointFBar2d, R}

        cylinder{PointFBar2a, PointFBar3a, R}
        cylinder{PointFBar2b, PointFBar3b, R}

        cylinder{PointFBar3c, PointFBar4c, R}
        cylinder{PointFBar3d, PointFBar4d, R}

        cylinder{PointFBar1a, PointJFaceA, R}
        cylinder{PointFBar1b, PointJFaceB, R}

        cylinder{PointJEndA, PointJEndB, R}
        cylinder{PointJEndB, PointJEndD, R}
        cylinder{PointJEndD, PointJEndC, R}
        cylinder{PointJEndC, PointJEndA, R}

        object{Tori}

        pigment{color DarkColor}

    }

    ///////////////////////////// JF compound as result of the macro

    union{
        object{LetterJFSolid}
        object{LetterJFOutlines}
        translate <0.85, -0.45, -0.25>
        scale .17
        rotate 90*y
    }

#end


///////////////////////////////////////////////// vertices, edges and faces of the truncated cuboctahedron

#declare Factor = .9;

#declare Abs = array[3]{ (1)*Factor, (1 + sqrt(2))*Factor, (1 + 2*sqrt(2))*Factor, }

#declare P = array[48]{ <-Abs[2],-Abs[1],-Abs[0]>, <-Abs[2],-Abs[1],Abs[0]>, <-Abs[2],-Abs[0],-Abs[1]>, <-Abs[2],-Abs[0],Abs[1]>, <-Abs[2],Abs[0],-Abs[1]>, <-Abs[2],Abs[0],Abs[1]>, <-Abs[2],Abs[1],-Abs[0]>, <-Abs[2],Abs[1],Abs[0]>, <-Abs[1],-Abs[2],-Abs[0]>, <-Abs[1],-Abs[2],Abs[0]>, <-Abs[1],-Abs[0],-Abs[2]>, <-Abs[1],-Abs[0],Abs[2]>, <-Abs[1],Abs[0],-Abs[2]>, <-Abs[1],Abs[0],Abs[2]>, <-Abs[1],Abs[2],-Abs[0]>, <-Abs[1],Abs[2],Abs[0]>, <-Abs[0],-Abs[2],-Abs[1]>, <-Abs[0],-Abs[2],Abs[1]>, <-Abs[0],-Abs[1],-Abs[2]>, <-Abs[0],-Abs[1],Abs[2]>, <-Abs[0],Abs[1],-Abs[2]>, <-Abs[0],Abs[1],Abs[2]>, <-Abs[0],Abs[2],-Abs[1]>, <-Abs[0],Abs[2],Abs[1]>, <Abs[0],-Abs[2],-Abs[1]>, <Abs[0],-Abs[2],Abs[1]>, <Abs[0],-Abs[1],-Abs[2]>, <Abs[0],-Abs[1],Abs[2]>, <Abs[0],Abs[1],-Abs[2]>, <Abs[0],Abs[1],Abs[2]>, <Abs[0],Abs[2],-Abs[1]>, <Abs[0],Abs[2],Abs[1]>, <Abs[1],-Abs[2],-Abs[0]>, <Abs[1],-Abs[2],Abs[0]>, <Abs[1],-Abs[0],-Abs[2]>, <Abs[1],-Abs[0],Abs[2]>, <Abs[1],Abs[0],-Abs[2]>, <Abs[1],Abs[0],Abs[2]>, <Abs[1],Abs[2],-Abs[0]>, <Abs[1],Abs[2],Abs[0]>, <Abs[2],-Abs[1],-Abs[0]>, <Abs[2],-Abs[1],Abs[0]>, <Abs[2],-Abs[0],-Abs[1]>, <Abs[2],-Abs[0],Abs[1]>, <Abs[2],Abs[0],-Abs[1]>, <Abs[2],Abs[0],Abs[1]>, <Abs[2],Abs[1],-Abs[0]>, <Abs[2],Abs[1],Abs[0]>, }

#declare DarkbrownVertices = array[24]{0, 3, 4, 7, 9, 10, 13, 14, 16, 19, 20, 23, 25, 26, 29, 30, 32, 35, 36, 39, 41, 42, 45, 46};

#declare LightbrownVertices = array[24]{1, 2, 5, 6, 8, 11, 12, 15, 17, 18, 21, 22, 24, 27, 28, 31, 33, 34, 37, 38, 40, 43, 44, 47};

#declare Edges = array[72]{array[2]{16, 24}, array[2]{43, 45}, array[2]{25, 33}, array[2]{46, 47}, array[2]{20, 28}, array[2]{11, 13}, array[2]{33, 41}, array[2]{18, 26}, array[2]{44, 46}, array[2]{5, 13}, array[2]{36, 44}, array[2]{11, 19}, array[2]{7, 15}, array[2]{2, 10}, array[2]{13, 21}, array[2]{34, 42}, array[2]{6, 14}, array[2]{10, 12}, array[2]{3, 11}, array[2]{9, 17}, array[2]{19, 27}, array[2]{35, 37}, array[2]{31, 39}, array[2]{40, 41}, array[2]{42, 44}, array[2]{29, 31}, array[2]{1, 3}, array[2]{25, 27}, array[2]{29, 37}, array[2]{5, 7}, array[2]{21, 29}, array[2]{45, 47}, array[2]{34, 36}, array[2]{24, 26}, array[2]{38, 39}, array[2]{23, 31}, array[2]{30, 38}, array[2]{12, 20}, array[2]{16, 18}, array[2]{8, 16}, array[2]{2, 4}, array[2]{21, 23}, array[2]{35, 43}, array[2]{28, 30}, array[2]{6, 7}, array[2]{37, 45}, array[2]{32, 40}, array[2]{41, 43}, array[2]{40, 42}, array[2]{14, 15}, array[2]{17, 19}, array[2]{24, 32}, array[2]{39, 47}, array[2]{4, 6}, array[2]{14, 22}, array[2]{26, 34}, array[2]{27, 35}, array[2]{28, 36}, array[2]{3, 5}, array[2]{0, 8}, array[2]{4, 12}, array[2]{10, 18}, array[2]{1, 9}, array[2]{15, 23}, array[2]{8, 9}, array[2]{22, 30}, array[2]{38, 46}, array[2]{0, 2}, array[2]{32, 33}, array[2]{20, 22}, array[2]{17, 25}, array[2]{0, 1}};

#declare Faces = array[26]{array[7]{P[9], P[17], P[19], P[11], P[3], P[1], P[9]}, array[9]{P[33], P[32], P[24], P[16], P[8], P[9], P[17], P[25], P[33]}, array[9]{P[43], P[41], P[40], P[42], P[44], P[46], P[47], P[45], P[43]}, array[9]{P[30], P[38], P[39], P[31], P[23], P[15], P[14], P[22], P[30]}, array[7]{P[5], P[13], P[21], P[23], P[15], P[7], P[5]}, array[5]{P[2], P[4], P[12], P[10], P[2]}, array[7]{P[31], P[29], P[37], P[45], P[47], P[39], P[31]}, array[9]{P[36], P[34], P[26], P[18], P[10], P[12], P[20], P[28], P[36]}, array[7]{P[18], P[16], P[8], P[0], P[2], P[10], P[18]}, array[7]{P[34], P[26], P[24], P[32], P[40], P[42], P[34]}, array[7]{P[28], P[30], P[38], P[46], P[44], P[36], P[28]}, array[7]{P[27], P[35], P[43], P[41], P[33], P[25], P[27]}, array[7]{P[4], P[6], P[14], P[22], P[20], P[12], P[4]}, array[5]{P[38], P[39], P[47], P[46], P[38]}, array[5]{P[0], P[8], P[9], P[1], P[0]}, array[9]{P[7], P[5], P[3], P[1], P[0], P[2], P[4], P[6], P[7]}, array[9]{P[35], P[37], P[29], P[21], P[13], P[11], P[19], P[27], P[35]}, array[5]{P[7], P[15], P[14], P[6], P[7]}, array[5]{P[32], P[33], P[41], P[40], P[32]}, array[5]{P[18], P[16], P[24], P[26], P[18]}, array[5]{P[5], P[13], P[11], P[3], P[5]}, array[5]{P[35], P[43], P[45], P[37], P[35]}, array[5]{P[34], P[36], P[44], P[42], P[34]}, array[5]{P[22], P[30], P[28], P[20], P[22]}, array[5]{P[21], P[23], P[31], P[29], P[21]}, array[5]{P[19], P[17], P[25], P[27], P[19]}};


union{

    union{
        #for( Index, 0, dimension_size(DarkbrownVertices, 1) - 1 )
            sphere{ P[DarkbrownVertices[Index]], RadVert }
        #end
        pigment{ color Darkbrown }
    }
    union{
        #for( Index, 0, dimension_size(LightbrownVertices, 1) - 1 )
            sphere{ P[LightbrownVertices[Index]], RadVert }
        #end
        pigment{ color Lightbrown }
    }

    union{
        #for( Index, 0, dimension_size(Edges, 1) - 1 )
            #local EdgeArray = Edges[Index];
            cylinder{ P[EdgeArray[0]], P[EdgeArray[1]], RadEdge }
        #end
        pigment{ color EdgeColor }
    }

    union{
        #for( Index, 0, dimension_size(Faces, 1) - 1 )
            #local FaceArray = Faces[Index];
            #local LenOfFaceArray = dimension_size(FaceArray, 1);
            polygon{ LenOfFaceArray,
                #for(VertexIndexInFace, 0, LenOfFaceArray-1)
                    FaceArray[VertexIndexInFace]
                #end
            }
        #end
        pigment{ color FaceColor }
    }

    scale .92
}


///////////////////////////////////////////////// ingredients to create the 24 rotations (light vertices)

// All 48 permutations of the full octahedral group are products of the ones in the two arrays below.
// The words 'row' and 'column' come from a context of left action, where r*c means c is executed first.
// Povray uses right action though, so to execute c first one has to write `transform{ c r }`.

#declare RowTransformations = array[8]{
    transform{ },
    transform{ scale -x },
    transform{ scale -z },
    transform{ rotate 180*y },
    transform{ scale -y },
    transform{ rotate 180*z },
    transform{ rotate 180*x },
    transform{ scale <-1, -1, -1> }
}

#declare ColTransformations = array[6]{
    transform{ },
    transform{ scale -z rotate -90*y },
    transform{ scale -y rotate -90*x },
    transform{ rotate 90*x rotate 90*z },
    transform{ rotate -90*z rotate -90*x },
    transform{ scale -x rotate -90*z }
}

// The following array contains the 24 pairs (r, c) for which r*c (or `transform{ c r }`) is an even permutation.

#declare RowCol = array[24]{
    array[2]{0, 0}, array[2]{0, 3}, array[2]{0, 4}, 
    array[2]{1, 1}, array[2]{1, 2}, array[2]{1, 5}, 
    array[2]{2, 1}, array[2]{2, 2}, array[2]{2, 5}, 
    array[2]{3, 0}, array[2]{3, 3}, array[2]{3, 4}, 
    array[2]{4, 1}, array[2]{4, 2}, array[2]{4, 5}, 
    array[2]{5, 0}, array[2]{5, 3}, array[2]{5, 4}, 
    array[2]{6, 0}, array[2]{6, 3}, array[2]{6, 4}, 
    array[2]{7, 1}, array[2]{7, 2}, array[2]{7, 5}
}


///////////////////////////////////////////////// permute and place the JF compounds

// even permutations (light)

#declare LetterJF = object{ 
    letterJF(Lightbrown)
    translate P[2]
}

#for( Index, 0, 23 )
    #local Row = RowCol[Index][0];
    #local Col = RowCol[Index][1];
    #local RowTrans = RowTransformations[Row];
    #local ColTrans = ColTransformations[Col];
    object{
        LetterJF
        transform{ ColTrans RowTrans }
    }
#end

// odd permutations (dark) as reflection of the even ones

#declare LetterJF = object{ 
    letterJF(Darkbrown)
    translate P[2]
}

union{
    #for( Index, 0, 23 )
        #local Row = RowCol[Index][0];
        #local Col = RowCol[Index][1];
        #local RowTrans = RowTransformations[Row];
        #local ColTrans = ColTransformations[Col];
        object{
            LetterJF
            transform{ ColTrans RowTrans }
        }
    #end
    scale -x
}

Istoricul fișierului

Apăsați pe Data și ora pentru a vedea versiunea trimisă atunci.

	Data și ora	Miniatură	Dimensiuni	Utilizator	Comentariu
actuală	25 februarie 2018 16:46		3.904x3.852 (686 KB)	Watchduck

Utilizarea fișierului

Următoarele pagini conțin această imagine:

Cuboctaedru trunchiat

Utilizarea globală a fișierului

Următoarele alte proiecte wiki folosesc acest fișier:

Utilizare la en.wikipedia.org
- Truncated cuboctahedron
Utilizare la en.wikiversity.org
- Full octahedral group

Informații

Acest fișier conține informații suplimentare, introduse probabil de aparatul fotografic digital sau scannerul care l-a generat. Dacă fișierul a fost modificat între timp, este posibil ca unele detalii să nu mai fie valabile.

Rezoluție orizontală	28,35 dpc
Rezoluție verticală	28,35 dpc
Data și ora modificării fișierului	25 februarie 2018 12:07
Comentarii la fișierul PNG	Render Date: 2018-02-25 03:46:56Z Platform: x86_64-pc-linux-gnu Compiler: g++ 5.2.1

Fișier:Full octahedral group elements in truncated cuboctahedron; JF.png

Descriere fișier

Licențiere

POV-Ray source

Captions

Items portrayed in this file

subiectul reprezentat

creator

some value

statutul drepturilor de autor

material protejat de drepturi de autor

licență

GNU Free Documentation License, version 1.2 or later ^engleză

CC BY 4.0

source of file ^engleză

original creation by uploader ^engleză

înființare

25 februarie 2018

tip MIME

image/png

Istoricul fișierului

Utilizarea fișierului

Utilizarea globală a fișierului

Informații

Descriere fișier

Licențiere

POV-Ray source

Captions

Items portrayed in this file

some value

GNU Free Documentation License, version 1.2 or later engleză

source of file engleză

original creation by uploader engleză

25 februarie 2018

image/png

Istoricul fișierului

Utilizarea fișierului

Utilizarea globală a fișierului

Informații

GNU Free Documentation License, version 1.2 or later ^engleză

source of file ^engleză

original creation by uploader ^engleză