@acer Thank you very much.

@acer 

How a bout this? I can not get the result?

restart;
with(PolyhedralSets):

ps := PolyhedralSets:-PolyhedralSet([[1/2,1/2,0],[-1/2,1/2,0],[-1/2,-1/2,0],[-1/4,1/4,sqrt(15)/4],[1/4,-1/4,sqrt(15)/4]],[x,y,z]):

@Kitonum Thank you very much. Can I get another list of vetors?

@mmcdara I want arithmetic progression version.

@vv Thank you very much. Now, it works.

@vv I copied your code, when I compile, I get "error, missing operation".

@Kitonum I added two conditions and igcd(a,b,c)=1 and igcd(x,y,z)=1. 

@vv Thank you very much.

@vv Thank you very much. It works.

@vv I got message 

@Kitonum How about this? -10<=b<=-1, ​​​​​​​-10<=d<=10, ​​​​​​​-10<=f<=10.

@vv Thank you very much.

@Kitonum Thank you very much.

@Kitonum How about  tetrahedron (1, 2, 3), (-2, 8, 9), (5, 0, 7), (3, 4, 2)?

@Kitonum I see. Thank you very much.