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File:Truncated cuboctahedron permutation 0 0.png

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Description
The original position corresponding to the neutral element
(The POV-Ray source is on that page.)
All elements of the group identified with vertices

One of the 48 elements of the full octahedral group, corresponding to one of the vertices of a truncated cuboctahedron.


 
This image was created with POV-Ray.
 
This file was uploaded with Commonist.


The black hexagon is this permutohedron, and the highlighted vertex is the neutral element of the group.
Date
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

Licensing edit

w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

POV-Ray source edit 

#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"


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

#declare Camera_Position = <12, 12, -45>;
camera{
    location Camera_Position
    right    x*image_width/image_height
    angle    11.7
    look_at  <-.12, -.13, 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 } }


///////////////////////////// truncated cuboctahedron

# declare SkeletonColor = White;

# declare Abs = array[3]{(1),(1 + sqrt(2)),(1 + 2*sqrt(2))}
# declare RadVert = .12;
# declare RadVertBig = .45;
# declare RadEdge = .05;
# 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 TrunCubOct = union {

    ///// vertices
    union{
    sphere{P[0],RadVert} sphere{P[1],RadVert} sphere{P[2],RadVert} sphere{P[3],RadVert} sphere{P[4],RadVert} sphere{P[5],RadVert} sphere{P[6],RadVert} sphere{P[7],RadVert} sphere{P[8],RadVert} sphere{P[9],RadVert} sphere{P[10],RadVert} sphere{P[11],RadVert} sphere{P[12],RadVert} sphere{P[13],RadVert} sphere{P[14],RadVert} sphere{P[15],RadVert} sphere{P[17],RadVert} sphere{P[18],RadVert} sphere{P[19],RadVert} sphere{P[20],RadVert} sphere{P[21],RadVert} sphere{P[22],RadVert} sphere{P[23],RadVert} sphere{P[24],RadVert} sphere{P[25],RadVert} sphere{P[26],RadVert} sphere{P[27],RadVert} sphere{P[28],RadVert} sphere{P[29],RadVert} sphere{P[30],RadVert} sphere{P[31],RadVert} sphere{P[32],RadVert} sphere{P[33],RadVert} sphere{P[34],RadVert} sphere{P[35],RadVert} sphere{P[36],RadVert} sphere{P[37],RadVert} sphere{P[38],RadVert} sphere{P[39],RadVert} sphere{P[40],RadVert} sphere{P[41],RadVert} sphere{P[42],RadVert} sphere{P[43],RadVert} sphere{P[44],RadVert} sphere{P[45],RadVert} sphere{P[46],RadVert} sphere{P[47],RadVert}
    pigment{color SkeletonColor}
    }

    ///// edges
    union{
    cylinder{P[38],P[39],RadEdge} cylinder{P[35],P[43],RadEdge} cylinder{P[14],P[22],RadEdge} cylinder{P[8],P[9],RadEdge} cylinder{P[21],P[29],RadEdge} cylinder{P[42],P[44],RadEdge} cylinder{P[40],P[41],RadEdge} cylinder{P[29],P[37],RadEdge} cylinder{P[36],P[44],RadEdge} cylinder{P[16],P[24],RadEdge} cylinder{P[38],P[46],RadEdge} cylinder{P[44],P[46],RadEdge} cylinder{P[43],P[45],RadEdge} cylinder{P[0],P[1],RadEdge} cylinder{P[25],P[33],RadEdge} cylinder{P[5],P[7],RadEdge} cylinder{P[25],P[27],RadEdge} cylinder{P[6],P[14],RadEdge} cylinder{P[10],P[18],RadEdge} cylinder{P[28],P[30],RadEdge} cylinder{P[34],P[42],RadEdge} cylinder{P[16],P[18],RadEdge} cylinder{P[35],P[37],RadEdge} cylinder{P[33],P[41],RadEdge} cylinder{P[10],P[12],RadEdge} cylinder{P[11],P[13],RadEdge} cylinder{P[5],P[13],RadEdge} cylinder{P[46],P[47],RadEdge} cylinder{P[39],P[47],RadEdge} cylinder{P[14],P[15],RadEdge} cylinder{P[4],P[12],RadEdge} cylinder{P[18],P[26],RadEdge} cylinder{P[12],P[20],RadEdge} cylinder{P[2],P[10],RadEdge} cylinder{P[19],P[27],RadEdge} cylinder{P[7],P[15],RadEdge} cylinder{P[1],P[9],RadEdge} cylinder{P[13],P[21],RadEdge} cylinder{P[8],P[16],RadEdge} cylinder{P[4],P[6],RadEdge} cylinder{P[3],P[11],RadEdge} cylinder{P[9],P[17],RadEdge} cylinder{P[29],P[31],RadEdge} cylinder{P[20],P[28],RadEdge} cylinder{P[24],P[32],RadEdge} cylinder{P[11],P[19],RadEdge} cylinder{P[3],P[5],RadEdge} cylinder{P[22],P[30],RadEdge} cylinder{P[41],P[43],RadEdge} cylinder{P[23],P[31],RadEdge} cylinder{P[26],P[34],RadEdge} cylinder{P[1],P[3],RadEdge} cylinder{P[28],P[36],RadEdge} cylinder{P[21],P[23],RadEdge} cylinder{P[32],P[40],RadEdge} cylinder{P[45],P[47],RadEdge} cylinder{P[34],P[36],RadEdge} cylinder{P[2],P[4],RadEdge} cylinder{P[37],P[45],RadEdge} cylinder{P[15],P[23],RadEdge} cylinder{P[31],P[39],RadEdge} cylinder{P[24],P[26],RadEdge} cylinder{P[32],P[33],RadEdge} cylinder{P[0],P[2],RadEdge} cylinder{P[30],P[38],RadEdge} cylinder{P[17],P[19],RadEdge} cylinder{P[20],P[22],RadEdge} cylinder{P[27],P[35],RadEdge} cylinder{P[6],P[7],RadEdge} cylinder{P[0],P[8],RadEdge} cylinder{P[40],P[42],RadEdge} cylinder{P[17],P[25],RadEdge}
    pigment{color SkeletonColor}
    }

    ///// highlighted elements

    sphere{P[16], RadVertBig   pigment{color SkeletonColor}   }

    polygon{9, P[33],P[32],P[24],P[16],P[8],P[9],P[17],P[25],P[33]    pigment{color rgbt<.33,.21,.08,.07>}    }
    polygon{7, P[18],P[16],P[8],P[0],P[2],P[10],P[18]    pigment{color rgbt<0,0,0,.05>}    }
    polygon{5, P[16],P[18],P[26],P[24],P[16]    pigment{color rgbt<.1,.029,.025,.07>}    }

}

object{
    TrunCubOct
    scale -x rotate -90*z
}

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current09:30, 20 December 2017Thumbnail for version as of 09:30, 20 December 20174,000 × 4,000 (1.33 MB)Watchduck (talk | contribs)

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