How to made my hexa like this??

Question

ahmed elnashar 2012-1-31

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/27638-how-to-made-my-hexa-like-this

编辑： Azzi Abdelmalek 2013-10-18

My code:

clc;  
close all
clear all;  
f=input('please enter the dim=')
t=linspace(0,2*pi,7);
for Z=[-f/2:1:f/2]
   for j=-f/2:1.732:f/2
    ao=((Z)*1.5)+1*cos(t);  
    bo=(j)+1*sin(t);  
    plot(ao,bo);  
    plot(Z*1.5,(j),'ro')
    hold on
   end
   for k=-f/2:1.732:f/2
    al=((-Z)*1.5)+1*cos(t);  
    bl=(k)+1*sin(t);  
    plot(al,bl);  
    plot(-Z*1.5,k,'ro')
    hold on   
   end
end

the result when I enter dim=10 is hexa generated but overlapping each other and I want it matching for planning.

[Information merged from first duplicate]

This code generate fixed area of hexa and i need to make it changable

clc; 
close all 
clear all; 
t=linspace(0,2*pi,7); 
ahx=0+1*cos(t); 
bhx=0+1*sin(t); 
plot(ahx,bhx); 
for i=-0.866:1.732:10 
ah=0+1*cos(t); 
bh=i+1*sin(t); 
plot(ah,bh); 
plot(0,i,'ro'); 
hold on 
end 
for j=1.732:1.732:10 
ar=1.5+1*cos(t); 
br=j+1*sin(t); 
plot(ar,br); 
plot(1.5,j,'ro') 
hold on 
end 
for k=1.732:1.732:10 
al=-1.5+1*cos(t); 
bl=k+1*sin(t); 
plot(al,bl); 
plot(-1.5,k,'ro') 
hold on 
end 
grid on

[Information merged from second duplicate]

i want to make this code with for loops and i cant change radius to any no except 1

close all
clear all
clc
%L=input('enter the length=')
r=input('enter the radius=')
        ax=-1.732            %middle
        ay=0
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on
        hold on
        ax=0
        ay=0
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'y')
        grid on
         hold on
        ax=1.732
        ay=0
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on
          ax=-1.732*2
        ay=0
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'b')
        grid on
        hold on
        ax=1.732*2
        ay=0
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'b')
        grid on
        ax=-1.732*3
        ay=0
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'y')
        grid on
        hold on
        ax=1.732*3
        ay=0
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on     %end
        ax=-1.732   %upper line
        ay=3*r
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on
        hold on
        ax=0
        ay=3*r
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'y')
        grid on
         hold on
        ax=1.732
        ay=3*r
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on
          ax=-1.732*2
        ay=3*r
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'b')
        grid on
        hold on
        ax=1.732*2
        ay=3*r
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'b')
        grid on
        ax=-1.732*3
        ay=3*r
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'y')
        grid on
        hold on
        ax=1.732*3
        ay=3*r
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on          %end
        ax=-1.732        %lower line
        ay=-3*r
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on
        hold on
        ax=0
        ay=-3*r
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'y')
        grid on
         hold on
        ax=1.732
        ay=-3*r
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on
          ax=-1.732*2
        ay=-3*r
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'b')
        grid on
        hold on
        ax=1.732*2
        ay=-3*r
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'b')
        grid on
        ax=-1.732*3
        ay=-3*r
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'y')
        grid on
        hold on
        ax=1.732*3
        ay=-3*r
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on                    %end
        ax=-0.866                 %first
        ay=1.5
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on
         hold on
        ax=0.866
        ay=1.5
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'b')
        grid on
          ax=-0.866*3
        ay=1.5
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'y')
        grid on
        hold on
        ax=0.866*3
        ay=1.5
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on
        ax=-0.866*5
        ay=1.5
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on
        hold on
        ax=0.866*5
        ay=1.5
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on                          %end
               ax=-0.866                 %second
        ay=-1.5
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on
         hold on
        ax=0.866
        ay=-1.5
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'b')
        grid on
          ax=-0.866*3
        ay=-1.5
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'y')
        grid on
        hold on
        ax=0.866*3
        ay=-1.5
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on
        ax=-0.866*5
        ay=-1.5
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on
        hold on
        ax=0.866*5
        ay=-1.5
        r1=sqrt(3)*r/2;
        r2=+(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on                      %end

[Information merged from 3rd duplicate]

i want to change radius and make always the center(0,0)

close all
clear all
clc
L=input('enter the length x=')
N=input('enter the length y=')
r=input('enter the radius=')
      for h=-(N)/2:3:(N)/2     
for i=-L/2:1.732:L/2   
           ax=i       %middle
        ay=h
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'r')
        grid on
        hold on
end 
      end
for j=-(N-3)/2:3:(N-3)/2
      for k=-(L+1.732)/2:1.732:(L+1.732)/2
           ax=k       %middle
        ay=j
        r1=sqrt(3)*r/2;
        r2=(r/2);
        A=[ax ay+r];
        B=[ax+r1 ay+r2]
        C=[ax+r1 ay-r2]
        D=[ax ay-r]
        E=[ax-r1 ay-r2]
        F=[ax-r1 ay+r2]
        x=[ax ax+r1 ax+r1 ax ax-r1 ax-r1];
        y=[ay+r ay+r2 ay-r2 ay-r ay-r2 ay+r2];
        fill(x,y,'g')
        grid on
        hold on
      end 
end

1 个评论
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Walter Roberson 2012-2-20

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Walter Roberson 2012-1-31

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/27638-how-to-made-my-hexa-like-this#answer_35888

在 MATLAB Online 中打开

t = linspace(0,2*pi,7);
f = input('please enter the (even) dim=')
clf
hold on
xlim([-f/2,f/2]);
ylim([-f/2,f/2]);
axis square
L = f/2 - 1;
Zp = -L : 2 : L;
jp = Zp * sqrt(3) / 2;
for Z = Zp
  for j = jp
    ao = Z + cos(t);
    bo = j + sin(t);
    plot(ao, bo);
    plot(Z, j, 'ro')
  end
end

Note: this graph will have the appearance that the hexagons are overlapped. They are not overlapped: it is an illusion that is partly generated because you wanted the hexagons lined up on a grid instead of being staggered like they are in a honeycomb.

2 个评论
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ahmed elnashar 2012-2-1

thank you but i still need it not overlapped the following code is generate hexa with fixed area :

clc;

close all

clear all;

t=linspace(0,2*pi,7);

ahx=0+1*cos(t);

bhx=0+1*sin(t);

plot(ahx,bhx);

for i=-0.866:1.732:10

ah=0+1*cos(t);

bh=i+1*sin(t);

plot(ah,bh);

plot(0,i,'ro');

hold on

end

for j=1.732:1.732:10

ar=1.5+1*cos(t);

br=j+1*sin(t);

plot(ar,br);

plot(1.5,j,'ro')

hold on

end

for k=1.732:1.732:10

al=-1.5+1*cos(t);

bl=k+1*sin(t);

plot(al,bl);

plot(-1.5,k,'ro')

hold on

end

grid on

SO,i need to make that area changable not fixed

thanks again for your answer and hope you help me with this

Walter Roberson 2012-2-1

The code I gave does NOT overlap anything. It might _look_ like it does, but that is an illusion because all the lines are the same color.

Here is a minor modification to the routine to change the coloring so that you can see more clearly that there is no overlap.

t = linspace(0,2*pi,7);

f = input('please enter the (even) dim=');

clf

hold on

xlim([-f/2,f/2]);

ylim([-f/2,f/2]);

axis square

L = f/2 - 1;

Zp = -L : 2 : L;

jp = Zp * sqrt(3) / 2;

colord = 'bgkcmy';

colidx = 0;

for Z = Zp

for j = jp

colidx = mod(colidx,length(colord)) + 1;

ao = Z + cos(t);

bo = j + sin(t);

plot(ao, bo, colord(colidx));

plot(Z, j, 'ro')

end

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Answer 2

Walter Roberson 2012-2-20

0
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Your duplicate questions have been merged in to your original question, and the duplicate questions have been deleted.

Before anyone can assist you, you need to give a clear description of what you are trying to achieve. For example,

"I am attempting to project a Hexadecachoronic Honeycomb to two dimensions, from the 4-dimensional viewpoint [v1,v2,v3,v4], looking towards [w1,w2,w3,w4], and [...]"