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This is a

Symmetry is

Please be happy, you all!ï»¿

**hexacosihedron**(600 faces). It was constructed with 3 kinds of different tetrahedra: 1,260-a + 912-b + 288-c [I constructed it on 15 Feb, 2012 at 19:40, the last in a long afternoon...] (lol)Symmetry is

**Th**(**tetrahedral complete**w. horiz. reflection)Please be happy, you all!ï»¿

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Seashell 02 (parametric surface)

It's unlikely to find such seashell in nature but...who cares? :-)

The attached script shows a way to fine-tune the protuberances distribution over each different shell shape (see the "th" function definition)

MathMod script:

{

"Param3D": {

"Description ": ["Seashell by Abderrahman Taha 19/04/2017"],

"Name": ["Sea Shells_003"],

"Component": ["Sea Shell"],

"Const": ["cu=0.001",

"cv=0.001",

"N=14",

"M=4",

"MaxU=pi",

"MinU=0",

"MaxV=5*pi/2",

"MinV=0",

"a=0.2",

"b=1",

"c=0.1",

"n=2"],

"Funct": [" th = 0.1* ( ( 1 - abs ( u-pi/2 ) / MaxU )

"DFxu=((Fx(u,v,t)-Fx(u+cu,v,t))/cu)",

"DFxv=((Fx(u,v,t)-Fx(u,v+cv,t))/cv)",

"DFyu=((Fy(u,v,t)-Fy(u+cu,v,t))/cu)",

"DFyv=((Fy(u,v,t)-Fy(u,v+cv,t))/cv)",

"DFzu=((Fz(u,v,t)-Fz(u+cu,v,t))/cu)",

"DFzv=((Fz(u,v,t)-Fz(u,v+cv,t))/cv)",

"n1=(DFyu(u,v,t)*DFzv(u,v,t)-DFzu(u,v,t)*DFyv(u,v,t))",

"n2=(DFzu(u,v,t)*DFxv(u,v,t)-DFxu(u,v,t)*DFzv(u,v,t))",

"n3=(DFxu(u,v,t)*DFyv(u,v,t)-DFyu(u,v,t)*DFxv(u,v,t))",

"Rapp=u/sqrt(u*u+v*v+t*t)",

"Fx=Fx(u,v,t)+th(u,v-3*t,t)*Rapp(n1(u,v,t),n2(u,v,t),n3(u,v,t))",

"Fy=Fy(u,v,t)+th(u,v-3*t,t)*Rapp(n2(u,v,t),n1(u,v,t),n3(u,v,t))",

"Fz=Fz(u,v,t)+th(u,v-3*t,t)*Rapp(n3(u,v,t),n1(u,v,t),n2(u,v,t))"],

"Fx": ["Fx(u,v,t)"],

"Fy": ["Fy(u,v,t)"],

"Fz": ["Fz(u,v,t)"],

"Umax": ["MaxU"],

"Umin": ["MinU"],

"Vmax": ["MaxV"],

"Vmin": ["MinV"]

}

}ï»¿

It's unlikely to find such seashell in nature but...who cares? :-)

The attached script shows a way to fine-tune the protuberances distribution over each different shell shape (see the "th" function definition)

MathMod script:

{

"Param3D": {

"Description ": ["Seashell by Abderrahman Taha 19/04/2017"],

"Name": ["Sea Shells_003"],

"Component": ["Sea Shell"],

"Const": ["cu=0.001",

"cv=0.001",

"N=14",

"M=4",

"MaxU=pi",

"MinU=0",

"MaxV=5*pi/2",

"MinV=0",

"a=0.2",

"b=1",

"c=0.1",

"n=2"],

"Funct": [" th = 0.1* ( ( 1 - abs ( u-pi/2 ) / MaxU )

**( v / MaxV + 0.05 ) * abs ( cos ( N * (u ) ) ^ 3 - sin ( N * ( v)) ^2 ) ) ^ 3",****" Fx = if ( M=1,2**(1-exp(u/(6*pi)))**cos(u)*cos(v/2)^2,if(M=2,((a**(1-v/(2*pi))**(1+cos(u))+c)*cos(n*v))*6+4,if(M=3,2^v**(sin(u)**cos(u))/35,if( M=4,1.2^v**(sin(u)^2*sin(v))+2,2*(1-exp(u/(6*pi)))**cos(u)*cos(v/2)^2))))",****" Fy = if ( M=1,2**(-1+exp(u/(6*pi)))**sin(u)*cos(v/2)^2,if(M=2,((a**(1-v/(2*pi))**(1+cos(u))+c)*sin(n*v))*6+4,if(M=3,2^v**(sin(u)^2*sin(v))/35-4,if(M=4,1.2^v*(sin(u)**cos(u))+5,2**(-1+exp(u/(6*pi)))**sin(u)*cos(v/2)^2))))",****" Fz = if ( M=1,1-exp(u/(3*pi))-sin(v)+exp(u/(6*pi))*sin(v),if(M=2,(b*v/(2*pi)+a**(1-v/(2*pi))**sin(u))*6-6,if(M=3,2^v**(sin(u)^2*cos(v))/35-12,if(M=4,1.2^v*(sin(u)^2*cos(v)) -12,1-exp(u/(3*pi))-sin(v)+exp(u/(6*pi))*sin(v)))))","DFxu=((Fx(u,v,t)-Fx(u+cu,v,t))/cu)",

"DFxv=((Fx(u,v,t)-Fx(u,v+cv,t))/cv)",

"DFyu=((Fy(u,v,t)-Fy(u+cu,v,t))/cu)",

"DFyv=((Fy(u,v,t)-Fy(u,v+cv,t))/cv)",

"DFzu=((Fz(u,v,t)-Fz(u+cu,v,t))/cu)",

"DFzv=((Fz(u,v,t)-Fz(u,v+cv,t))/cv)",

"n1=(DFyu(u,v,t)*DFzv(u,v,t)-DFzu(u,v,t)*DFyv(u,v,t))",

"n2=(DFzu(u,v,t)*DFxv(u,v,t)-DFxu(u,v,t)*DFzv(u,v,t))",

"n3=(DFxu(u,v,t)*DFyv(u,v,t)-DFyu(u,v,t)*DFxv(u,v,t))",

"Rapp=u/sqrt(u*u+v*v+t*t)",

"Fx=Fx(u,v,t)+th(u,v-3*t,t)*Rapp(n1(u,v,t),n2(u,v,t),n3(u,v,t))",

"Fy=Fy(u,v,t)+th(u,v-3*t,t)*Rapp(n2(u,v,t),n1(u,v,t),n3(u,v,t))",

"Fz=Fz(u,v,t)+th(u,v-3*t,t)*Rapp(n3(u,v,t),n1(u,v,t),n2(u,v,t))"],

"Fx": ["Fx(u,v,t)"],

"Fy": ["Fy(u,v,t)"],

"Fz": ["Fz(u,v,t)"],

"Umax": ["MaxU"],

"Umin": ["MinU"],

"Vmax": ["MaxV"],

"Vmin": ["MinV"]

}

}ï»¿

‹

›

19/04/2017

4 Photos - View album

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This little solid (fig 1) is a

Please compare this with this other solid (fig. 2) composed of

The symmetry of both solids is

Please be well, everyone & enjoy springtime (in your lives!..)ï»¿

**space-filler**: it is formed of**12 tetrakaidecahedra**plus 8 non regular**dodecahedra**(in red), both the h14 & the h12 appearing in the celebrated**Weaire-Phelan**structure which I posted here some time ago.Please compare this with this other solid (fig. 2) composed of

**24 tetrakaidecahedra**& 9 non regular**dodecahedra**(the dodecs are in red & there is one at the center). This is the celebrated**Clathrate type I**(that I also posted in this bunch some time ago)The symmetry of both solids is

**Th**(**tetrahedral complete**w. horiz reflection)Please be well, everyone & enjoy springtime (in your lives!..)ï»¿

4/18/17

2 Photos - View album

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Fly through a cubic fractal (the "Menger sponge") and watch it split apart.ï»¿

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Seashell (parametric surface)

Looking for a more realistic Seashell model by using trigonometric expressions for the protuberance.

MathMod script:

{

"Param3D": {

"Description ": ["SeaShell by Abderrahman Taha 16/04/2017"],

"Name": ["SeaShell_001"],

"Component": ["SeaShell"],

"Const": ["cu=0.001",

"cv=0.001",

"N=5",

"M=3",

"MaxU=6*pi",

"MinU=0",

"MaxV=2*pi",

"MinV=0",

"a=0.2",

"b=1",

"c=0.1",

"n=2"],

"Funct": ["th=-(((u)/MaxU+0.05 ) * 0.4*abs(cos(7*(u))^3 - sin(7*(v))^2 ))^3",

"Fx=2*(1-exp(u/(6*pi))) * cos(u) * cos(v/2)^2",

"Fy=2*(-1+exp(u/(6*pi))) * sin(u) * cos(v/2)^2",

"Fz=1-exp(u/(3*pi))-sin(v)+exp(u/(6*pi)) *sin(v)",

"DFxu=((Fx(u,v,t)-Fx(u+cu,v,t))/cu)",

"DFxv=((Fx(u,v,t)-Fx(u,v+cv,t))/cv)",

"DFyu=((Fy(u,v,t)-Fy(u+cu,v,t))/cu)",

"DFyv=((Fy(u,v,t)-Fy(u,v+cv,t))/cv)",

"DFzu=((Fz(u,v,t)-Fz(u+cu,v,t))/cu)",

"DFzv=((Fz(u,v,t)-Fz(u,v+cv,t))/cv)",

"n1=(DFyu(u,v,t)*DFzv(u,v,t)-DFzu(u,v,t)*DFyv(u,v,t))",

"n2=(DFzu(u,v,t)*DFxv(u,v,t)-DFxu(u,v,t)*DFzv(u,v,t))",

"n3=(DFxu(u,v,t)*DFyv(u,v,t)-DFyu(u,v,t)*DFxv(u,v,t))",

"Rapp=u/sqrt(u*u+v*v+t*t)",

"Fx=Fx(u,v,t)+th(u,v-3*t,t)*Rapp(n1(u,v,t),n2(u,v,t),n3(u,v,t))",

"Fy=Fy(u,v,t)+th(u,v-3*t,t)*Rapp(n2(u,v,t),n1(u,v,t),n3(u,v,t))",

"Fz=Fz(u,v,t)+th(u,v-3*t,t)*Rapp(n3(u,v,t),n1(u,v,t),n2(u,v,t))"],

"Fx": ["-Fx(u,v,t)"],

"Fy": ["Fy(u,v,t)"],

"Fz": ["Fz(u,v,t)"],

"Umax": ["MaxU"],

"Umin": ["MinU"],

"Vmax": ["MaxV"],

"Vmin": ["MinV"]

}

}ï»¿

Looking for a more realistic Seashell model by using trigonometric expressions for the protuberance.

MathMod script:

{

"Param3D": {

"Description ": ["SeaShell by Abderrahman Taha 16/04/2017"],

"Name": ["SeaShell_001"],

"Component": ["SeaShell"],

"Const": ["cu=0.001",

"cv=0.001",

"N=5",

"M=3",

"MaxU=6*pi",

"MinU=0",

"MaxV=2*pi",

"MinV=0",

"a=0.2",

"b=1",

"c=0.1",

"n=2"],

"Funct": ["th=-(((u)/MaxU+0.05 ) * 0.4*abs(cos(7*(u))^3 - sin(7*(v))^2 ))^3",

"Fx=2*(1-exp(u/(6*pi))) * cos(u) * cos(v/2)^2",

"Fy=2*(-1+exp(u/(6*pi))) * sin(u) * cos(v/2)^2",

"Fz=1-exp(u/(3*pi))-sin(v)+exp(u/(6*pi)) *sin(v)",

"DFxu=((Fx(u,v,t)-Fx(u+cu,v,t))/cu)",

"DFxv=((Fx(u,v,t)-Fx(u,v+cv,t))/cv)",

"DFyu=((Fy(u,v,t)-Fy(u+cu,v,t))/cu)",

"DFyv=((Fy(u,v,t)-Fy(u,v+cv,t))/cv)",

"DFzu=((Fz(u,v,t)-Fz(u+cu,v,t))/cu)",

"DFzv=((Fz(u,v,t)-Fz(u,v+cv,t))/cv)",

"n1=(DFyu(u,v,t)*DFzv(u,v,t)-DFzu(u,v,t)*DFyv(u,v,t))",

"n2=(DFzu(u,v,t)*DFxv(u,v,t)-DFxu(u,v,t)*DFzv(u,v,t))",

"n3=(DFxu(u,v,t)*DFyv(u,v,t)-DFyu(u,v,t)*DFxv(u,v,t))",

"Rapp=u/sqrt(u*u+v*v+t*t)",

"Fx=Fx(u,v,t)+th(u,v-3*t,t)*Rapp(n1(u,v,t),n2(u,v,t),n3(u,v,t))",

"Fy=Fy(u,v,t)+th(u,v-3*t,t)*Rapp(n2(u,v,t),n1(u,v,t),n3(u,v,t))",

"Fz=Fz(u,v,t)+th(u,v-3*t,t)*Rapp(n3(u,v,t),n1(u,v,t),n2(u,v,t))"],

"Fx": ["-Fx(u,v,t)"],

"Fy": ["Fy(u,v,t)"],

"Fz": ["Fz(u,v,t)"],

"Umax": ["MaxU"],

"Umin": ["MinU"],

"Vmax": ["MaxV"],

"Vmin": ["MinV"]

}

}ï»¿

‹

›

16/04/2017

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