Fichier:Hexahedron.jpg
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Taille de cet aperçu : 538 × 599 pixels. Autres résolutions : 216 × 240 pixels | 431 × 480 pixels | 742 × 826 pixels.
Fichier d’origine (742 × 826 pixels, taille du fichier : 51 kio, type MIME : image/jpeg)
Description
| Description |
English: A Hexahedron (cube). A regular polyhedron. |
| Source | see below |
| Auteur | Original téléversé par Cyp sur Wikipédia anglais. |
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Une version vectorielle de cette image existe, dans le format « SVG ». Si elle n’est pas inférieure, elle devrait être utilisée à la place de la présente version pour des affichages en plus grandes dimensions ou nécessitant une meilleure résolution.
File:Hexahedron.jpg → File:Hexahedron.svg
Pour plus d’informations sur les images vectorielles, consultez la page de transition de Commons vers le format SVG. Voir aussi les informations à propos de la manière dont le logiciel MediaWiki gère les images au format SVG. |
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Conditions d’utilisation
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Vous avez la permission de copier, distribuer et modifier ce document selon les termes de la GNU Free Documentation License version 1.2 ou toute version ultérieure publiée par la Free Software Foundation, sans sections inaltérables, sans texte de première page de couverture et sans texte de dernière page de couverture. Un exemplaire de la licence est inclus dans la section intitulée GNU Free Documentation License. |
  
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Ce fichier est disponible selon les termes de la licence Creative Commons Attribution – Partage dans les Mêmes Conditions 3.0 Non Transposé. | |
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| Ce bandeau de licence a été ajouté à ce fichier dans le cadre de la procédure de mise à jour des licences des images sous GFDL. |
Povray src code
Hexahedron, made by me using POV-Ray, see en:User:Cyp/Poly.pov for source.}}
//Picture *** Use flashiness=1 !!! ***
//
// +w1024 +h1024 +a0.3 +am2
// +w512 +h512 +a0.3 +am2
//
//Movie *** Use flashiness=0.25 !!! ***
//
// +kc +kff120 +w256 +h256 +a0.3 +am2
// +kc +kff60 +w256 +h256 +a0.3 +am2
//"Fast" preview
// +w128 +h128
#declare notwireframe=1;
#declare withreflection=0;
#declare flashiness=0.25; //Still pictures use 1, animated should probably be about 0.25.
#macro This_shape_will_be_drawn()
//PLATONIC SOLIDS ***********
//tetrahedron() #declare rotation=seed(1889/*1894*/);
//hexahedron() #declare rotation=seed(7122);
//octahedron() #declare rotation=seed(4193);
//dodecahedron() #declare rotation=seed(4412);
//icosahedron() #declare rotation=seed(7719);
//weirdahedron() #declare rotation=seed(7412);
//ARCHIMEDIAN SOLIDS ***********
//cuboctahedron() #declare rotation=seed(1941);
//icosidodecahedron() #declare rotation=seed(2241);
//truncatedtetrahedron() #declare rotation=seed(8717);
//truncatedhexahedron() #declare rotation=seed(1345);
//truncatedoctahedron() #declare rotation=seed(7235);
//truncateddodecahedron() #declare rotation=seed(9374);
//truncatedicosahedron() #declare rotation=seed(1666);
//rhombicuboctahedron() #declare rotation=seed(6124);
//truncatedcuboctahedron() #declare rotation=seed(1156);
//rhombicosidodecahedron() #declare rotation=seed(8266);
//truncatedicosidodecahedron() #declare rotation=seed(1422);
//snubhexahedron(-1) #declare rotation=seed(7152);
//snubhexahedron(1) #declare rotation=seed(1477);
//snubdodecahedron(-1) #declare rotation=seed(5111);
//snubdodecahedron(1) #declare rotation=seed(8154);
//CATALAN SOLIDS ***********
//rhombicdodecahedron() #declare rotation=seed(7154);
//rhombictriacontahedron() #declare rotation=seed(1237);
//triakistetrahedron() #declare rotation=seed(7735);
//triakisoctahedron() #declare rotation=seed(5354);
//tetrakishexahedron() #declare rotation=seed(1788);
//triakisicosahedron() #declare rotation=seed(1044);
//pentakisdodecahedron() #declare rotation=seed(6100);
//deltoidalicositetrahedron() #declare rotation=seed(5643);
//disdyakisdodecahedron() #declare rotation=seed(1440);
//deltoidalhexecontahedron() #declare rotation=seed(1026);
//disdyakistriacontahedron() #declare rotation=seed(1556);
//pentagonalicositetrahedron(-1) #declare rotation=seed(7771);
//pentagonalicositetrahedron(1) #declare rotation=seed(3470);
//pentagonalhexecontahedron(-1) #declare rotation=seed(1046);
//pentagonalhexecontahedron(1) #declare rotation=seed(1096);
//PRISMS, ANTIPRISMS, ETC... ***********
//rprism(5) #declare rotation=seed(6620);
antiprism(5) #declare rotation=seed(6620);
//bipyramid(5) #declare rotation=seed(6620);
//trapezohedron(17) #declare rotation=seed(6620);
#end
#declare tau=(1+sqrt(5))/2;
#declare sq2=sqrt(2);
#declare sq297=sqrt(297);
#declare xi=(pow(sq297+17,1/3)-pow(sq297-17,1/3)-1)/3;
#declare sqweird=sqrt(tau-5/27);
#declare ouch=pow((tau+sqweird)/2,1/3)+pow((tau-sqweird)/2,1/3);
#declare alfa=ouch-1/ouch;
#declare veta=(ouch+tau+1/ouch)*tau;
#macro tetrahedron()
addpointsevensgn(<1,1,1>)
autoface()
#end
#macro hexahedron()
addpointssgn(<1,1,1>,<1,1,1>)
autoface()
#end
#macro octahedron()
addevenpermssgn(<1,0,0>,<1,0,0>)
autoface()
#end
#macro dodecahedron()
addpointssgn(<1,1,1>,<1,1,1>)
addevenpermssgn(<0,1/tau,tau>,<0,1,1>)
autoface()
#end
#macro icosahedron()
addevenpermssgn(<0,1,tau>,<0,1,1>)
autoface()
#end
#macro weirdahedron()
addpermssgn(<1,2,3>,<1,1,1>)
autoface()
#end
#macro cuboctahedron()
addevenpermssgn(<0,1,1>,<0,1,1>)
autoface()
#end
#macro icosidodecahedron()
addevenpermssgn(<0,0,2*tau>,<0,0,1>)
addevenpermssgn(<1,tau,1+tau>,<1,1,1>)
autoface()
#end
#macro truncatedtetrahedron()
addevenpermsevensgn(<1,1,3>)
autoface()
#end
#macro truncatedhexahedron()
addevenpermssgn(<sq2-1,1,1>,<1,1,1>)
autoface()
#end
#macro truncatedoctahedron()
addpermssgn(<0,1,2>,<0,1,1>)
autoface()
#end
#macro truncateddodecahedron()
addevenpermssgn(<0,1/tau,2+tau>,<0,1,1>)
addevenpermssgn(<1/tau,tau,2*tau>,<1,1,1>)
addevenpermssgn(<tau,2,1+tau>,<1,1,1>)
autoface()
#end
#macro truncatedicosahedron()
addevenpermssgn(<0,1,3*tau>,<0,1,1>)
addevenpermssgn(<2,1+2*tau,tau>,<1,1,1>)
addevenpermssgn(<1,2+tau,2*tau>,<1,1,1>)
autoface()
#end
#macro rhombicuboctahedron()
addevenpermssgn(<1+sq2,1,1>,<1,1,1>)
autoface()
#end
#macro truncatedcuboctahedron()
addpermssgn(<1,1+sq2,1+sq2*2>,<1,1,1>)
autoface()
#end
#macro rhombicosidodecahedron()
addevenpermssgn(<1,1,1+2*tau>,<1,1,1>)
addevenpermssgn(<tau,2*tau,1+tau>,<1,1,1>)
addevenpermssgn(<2+tau,0,1+tau>,<1,0,1>)
autoface()
#end
#macro truncatedicosidodecahedron()
addevenpermssgn(<1/tau,1/tau,3+tau>,<1,1,1>)
addevenpermssgn(<2/tau,tau,1+2*tau>,<1,1,1>)
addevenpermssgn(<1/tau,1+tau,3*tau-1>,<1,1,1>)
addevenpermssgn(<2*tau-1,2,2+tau>,<1,1,1>)
addevenpermssgn(<tau,3,2*tau>,<1,1,1>)
autoface()
#end
#macro snubhexahedron(s)
addpermsaltsgn(<1,1/xi,xi>*s)
autoface()
#end
#macro snubdodecahedron(s)
addevenpermsevensgn(<2*alfa,2,2*veta>*s)
addevenpermsevensgn(<alfa+veta/tau+tau,-alfa*tau+veta+1/tau,alfa/tau+veta*tau-1>*s)
addevenpermsevensgn(<-alfa/tau+veta*tau+1,-alfa+veta/tau-tau,alfa*tau+veta-1/tau>*s)
addevenpermsevensgn(<-alfa/tau+veta*tau-1,alfa-veta/tau-tau,alfa*tau+veta+1/tau>*s)
addevenpermsevensgn(<alfa+veta/tau-tau,alfa*tau-veta+1/tau,alfa/tau+veta*tau+1>*s)
autoface()
#end
#macro rhombicdodecahedron()
cuboctahedron() dual()
#end
#macro rhombictriacontahedron()
icosidodecahedron() dual()
#end
#macro triakistetrahedron()
truncatedtetrahedron() dual()
#end
#macro triakisoctahedron()
truncatedhexahedron() dual()
#end
#macro tetrakishexahedron()
truncatedoctahedron() dual()
#end
#macro triakisicosahedron()
truncateddodecahedron() dual()
#end
#macro pentakisdodecahedron()
truncatedicosahedron() dual()
#end
#macro deltoidalicositetrahedron()
rhombicuboctahedron() dual()
#end
#macro disdyakisdodecahedron()
truncatedcuboctahedron() dual()
#end
#macro deltoidalhexecontahedron()
rhombicosidodecahedron() dual()
#end
#macro disdyakistriacontahedron()
truncatedicosidodecahedron() dual()
#end
#macro pentagonalicositetrahedron(s)
snubhexahedron(s) dual()
#end
#macro pentagonalhexecontahedron(s)
snubdodecahedron(s) dual()
#end
#macro rprism(n)
#local a=sqrt((1-cos(2*pi/n))/2);
#local b=0; #while(b<n-.5)
addpointssgn(<sin(2*pi*b/n),cos(2*pi*b/n),a>,<0,0,1>)
#local b=b+1; #end
autoface()
#end
#macro antiprism(n)
#local a=sqrt((cos(pi/n)-cos(2*pi/n))/2);
#local b=0; #while(b<2*n-.5)
addpoint(<sin(pi*b/n),cos(pi*b/n),a>)
#local a=-a; #local b=b+1; #end
autoface()
#end
#macro bipyramid(n)
rprism(n) dual()
#end
#macro trapezohedron(n)
antiprism(n) dual()
#end
#declare points=array[1000];
#declare npoints=0;
#declare faces=array[1000];
#declare nfaces=0;
#macro addpoint(a)
#declare points[npoints]=a;
#declare npoints=npoints+1;
#end
#macro addevenperms(a)
addpoint(a)
addpoint(<a.y,a.z,a.x>)
addpoint(<a.z,a.x,a.y>)
#end
#macro addperms(a)
addevenperms(a)
addevenperms(<a.x,a.z,a.y>)
#end
#macro addpointssgn(a,s)
addpoint(a)
#if(s.x) addpointssgn(a*<-1,1,1>,s*<0,1,1>) #end
#if(s.y) addpointssgn(a*<1,-1,1>,s*<0,0,1>) #end
#if(s.z) addpoint(a*<1,1,-1>) #end
#end
#macro addevenpermssgn(a,s)
addpointssgn(a,s)
addpointssgn(<a.y,a.z,a.x>,<s.y,s.z,s.x>)
addpointssgn(<a.z,a.x,a.y>,<s.z,s.x,s.y>)
#end
#macro addpermssgn(a,s)
addevenpermssgn(a,s)
addevenpermssgn(<a.x,a.z,a.y>,<s.x,s.z,s.y>)
#end
#macro addpointsevensgn(a)
addpoint(a)
addpoint(a*<-1,-1,1>)
addpoint(a*<-1,1,-1>)
addpoint(a*<1,-1,-1>)
#end
#macro addevenpermsevensgn(a)
addevenperms(a)
addevenperms(a*<-1,-1,1>)
addevenperms(a*<-1,1,-1>)
addevenperms(a*<1,-1,-1>)
#end
#macro addpermsaltsgn(a)
addevenpermsevensgn(a)
addevenpermsevensgn(<a.x,a.z,-a.y>)
#end
/*#macro addevenpermssgn(a,s) //Calls addevenperms with, for each 1 in s, a.{x,y,z} replaced with {+,-}a.{x,y,z}
addevenperms(a)
#if(s.x) addevenpermssgn(a*<-1,1,1>,s*<0,1,1>) #end
#if(s.y) addevenpermssgn(a*<1,-1,1>,s*<0,0,1>) #end
#if(s.z) addevenperms(a*<1,1,-1>) #end
#end*/
#macro addface(d,l)
#local a=vnormalize(d)/l;
#local f=1;
#local n=0; #while(n<nfaces-.5)
#if(vlength(faces[n]-a)<0.00001) #local f=0; #end
#local n=n+1; #end
#if(f)
#declare faces[nfaces]=a;
#declare nfaces=nfaces+1;
#end
#end
#macro dual()
#declare temp=faces;
#declare faces=points;
#declare points=temp;
#declare temp=nfaces;
#declare nfaces=npoints;
#declare npoints=temp;
#end
#macro autoface() //WARNING: ONLY WORKS IF ALL EDGES HAVE EQUAL LENGTH
//Find edge length
#declare elength=1000;
#local a=0; #while(a<npoints-.5) #local b=0; #while(b<npoints-.5)
#local c=vlength(points[a]-points[b]); #if(c>0.00001 & c<elength) #local elength=c; #end
#local b=b+1; #end #local a=a+1; #end
//Find planes
//#macro planes()
#local a=0; #while(a<npoints-.5)
#local b=a+1; #while(b<npoints-.5)
#if(vlength(points[a]-points[b])<elength+0.00001) #local c=b+1; #while(c<npoints-.5)
#if(vlength(points[a]-points[c])<elength+0.00001)
#local n=vnormalize(vcross(points[b]-points[a],points[c]-points[a]));
#local d=vdot(n,points[a]);
#if(d<0) #local n=-n; #local d=-d; #end
#local f=1;
#local e=0; #while(e<npoints-.5)
#if(vdot(n, points[e])>d+0.00001) #local f=0; #end
#local e=e+1; #end
#if(f)
#declare ld=d;
addface(n,d) //plane { n, d }
#end
#end
#local c=c+1; #end #end
#local b=b+1; #end
#local a=a+1; #end
#end
This_shape_will_be_drawn()
//Random rotations are (hopefully) equally distributed...
#declare rot1=rand(rotation)*pi*2;
#declare rot2=acos(1-2*rand(rotation));
#declare rot3=(rand(rotation)+clock)*pi*2;
#macro dorot()
rotate rot1*180/pi*y
rotate rot2*180/pi*x
rotate rot3*180/pi*y
#end
//Scale shape to fit in unit sphere
#local b=0;
#local a=0; #while(a<npoints-.5)
#local c=vlength(points[a]); #if(c>b) #local b=c; #end
#local a=a+1; #end
#local a=0; #while(a<npoints-.5)
#local points[a]=points[a]/b;
#local a=a+1; #end
#local a=0; #while(a<nfaces-.5)
#local faces[a]=faces[a]*b;
#local a=a+1; #end
//Draw edges
#macro addp(a)
#declare p[np]=a;
#declare np=np+1;
#end
#local a=0; #while(a<nfaces-.5)
#declare p=array[20];
#declare np=0;
#local b=0; #while(b<npoints-.5)
#if(vdot(faces[a],points[b])>1-0.00001) addp(b) #end
#local b=b+1; #end
#local c=0; #while(c<np-.5)
#local d=0; #while(d<np-.5) #if(p[c]<p[d]-.5)
#local f=1;
#local e=0; #while(e<np-.5) #if(e!=c & e!=d & vdot(vcross(points[p[c]],points[p[d]]),points[p[e]])<0)
#local f=0;
#end #local e=e+1; #end
#if(f)
object {
cylinder { points[p[c]], points[p[d]], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#end #end
#local d=d+1; #end
#local c=c+1; #end
#local a=a+1; #end
/*#local a=0; #while(a<npoints-.5)
#local b=a+1; #while(b<npoints-.5)
#if(vlength(points[a]-points[b])<elength+0.00001)
object {
cylinder { points[a], points[b], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#end
#local b=b+1; #end
#local a=a+1; #end*/
//Draw points
#local a=0; #while(a<npoints-.5)
object {
sphere { points[a], .01 dorot() }
pigment { colour <.3,.3,.3> }
finish { ambient 0 diffuse 1 phong 1 }
}
#local a=a+1; #end
#if(notwireframe)
//Draw planes
object {
intersection {
#local a=0; #while(a<nfaces-.5)
plane { faces[a], 1/vlength(faces[a]) }
#local a=a+1; #end
//planes()
//sphere { <0,0,0>, 1 }
//sphere { <0,0,0>, ld+.01 inverse }
dorot()
}
pigment { colour rgbt <.8,.8,.8,.4> }
finish { ambient 0 diffuse 1 phong flashiness #if(withreflection) reflection { .2 } #end }
//interior { ior 1.5 }
photons {
target on
refraction on
reflection on
collect on
}
}
#end
// CCC Y Y PP
// C Y Y P P
// C Y PP
// C Y P
// CCC Y P
#local a=0;
#while(a<11.0001)
light_source { <4*sin(a*pi*2/11), 5*cos(a*pi*6/11), -4*cos(a*pi*2/11)> colour (1+<sin(a*pi*2/11),sin(a*pi*2/11+pi*2/3),sin(a*pi*2/11+pi*4/3)>)*2/11 }
#local a=a+1;
#end
background { color <1,1,1> }
camera {
perspective
location <0,0,0>
direction <0,0,1>
right x/2
up y/2
sky <0,1,0>
location <0,0,-4.8>
look_at <0,0,0>
}
global_settings {
max_trace_level 40
photons {
count 200000
autostop 0
}
}
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Une version vectorielle de cette image existe, dans le format « SVG ». Elle devrait être utilisée à la place de cette image matricielle.
File:Hexahedron.jpg → File:Hexahedron.svg
Pour plus d’informations sur les images vectorielles, consultez la page de transition de Commons vers le format SVG. Voir aussi les informations à propos de la manière dont le logiciel MediaWiki gère les images au format SVG. |
|
Historique du fichier
Cliquer sur une date et heure pour voir le fichier tel qu'il était à ce moment-là.
| Date et heure | Vignette | Dimensions | Utilisateur | Commentaire | |
|---|---|---|---|---|---|
| actuel | 6 janvier 2005 à 21:28 | | 742 × 826 (51 kio) | wikimediacommons>Kjell André | A Hexahedron (cube). A regular polyhedron. |
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