ListVectorPlot3D not plotting anything nor giving any error, just empty 3D axes

Question

It's as simple as the title says. My code is:

b1 = 2 Pi/a {1/Sqrt[3], 1, 0};
b2 = 2 Pi/a {1/Sqrt[3], -1, 0};
b3 = -2 Pi/c {0, 0, 1};

KK[n1_, n2_, n3_] = n1 b1 + n2 b2 + n3 b3;

lista1 = Table[{KK[n1, n2, n3], b1}, {n1, 0, 5, 1}, {n2, 0, 5, 
    1}, {n3, 0, 5, 1}];

reemp = {a -> 2, c -> 1};

l1 = lista1 /. reemp;
l2 = lista2 /. reemp;
l3 = lista3 /. reemp;

ListVectorPlot3D[l1, VectorPoints -> All]

I compare it whith the manual's ("Get Help" option) working example:

vectors = Table[{{x, y, z}, {y, x - x^3, z}}, {x, -1.5, 1.5, 0.2}, {y, -2, 2,0.2}, {z, -1, 1,0.1}];
ListVectorPlot3D[vectors];

but can't find any significant difference in terms of code. Also tried using the option "VectorPoints -> All", but with no avail. I read some past answers but found nothing i could use. The most similar question i could find is this 8-year-old wolfram's forum question

but there they don't really solve the problem. Maybe nowadays there's finally an answer!

EDIT: the idea is to have the vectors $b_i$ plotted at KK sites

Forgot to mention that i also tried this other implementation that does plot something, but not what i want...the vectors doesn't seem to be located at the points positions

n1max = 3 ; n2max = 3 ; n3max = 3;
pason1 = 1; pason2 = 1; pason3 = 1;

posiciones = Flatten[Table[KK[n1, n2, n3], {n1, 0, n1max, pason1}, {n2, 0, n2max,pason2}, {n3, 0, n3max, pason3}], 2];

lista1 = Table[b1, {n1, 0, n1max, pason1}, {n2, 0, n2max, pason2}, {n3, 0, n3max,pason3}];

reemp = {a -> 2, c -> 1};

l1 = lista1 /. reemp;
l2 = lista2 /. reemp;
l3 = lista3 /. reemp;

prom = Mean[{2 Pi/a, 2 Pi/c} /. reemp];

g1 = ListPointPlot3D[posiciones /. reemp];
gv1 = ListVectorPlot3D[l1,DataRange -> {{0, n1max Norm[b1]}, {0, n2max Norm[b2]}, {0,n3max Norm[b3]}} /. reemp, VectorScale -> Small];
Show[g1, gv1]

Also I'd like the arrows to start at the position dots and extend to the corresponding next dots... something like: o->o

Answer 1

The third bullet point in the documentation for ListVectorPlot3D states:

ListVectorPlot3D by default interpolates the data given and plots vectors for the vector field at a regular 3D grid of positions.

Diving into the code for ListVectorPlot3D reveals that it uses Interpolation on the (reshaped) data. For example:

regularGrid = Table[{{x, y, z}, {1, 1, 1}}, {x, 5}, {y, 5}, {z, 5}];
irregularGrid = Table[{{x, 2 x + y, z}, {1, 1, 1}}, {x, 5}, {y, 5}, {z, 5}];

Interpolation[Flatten[regularGrid, {{1, 2, 3}}]]
(* Works as expected *)

Interpolation[Flatten[irregularGrid, {{1, 2, 3}}]]
(* Interpolation::udeg : Interpolation on unstructured grids is currently only supported 
   for InterpolationOrder->1 or InterpolationOrder->All. Order will be reduced to 1 *)

Even by changing InterpolationOrder->All in the code, I did not manage to produce a plot. Luckily, however, you don't really want any interpolation because you are plotting a constant vector field. Therefore, you can simply use VectorPlot3D together with VectorPoints.

b1 = 2 Pi/a {1/Sqrt[3], 1, 0};
b2 = 2 Pi/a {1/Sqrt[3], -1, 0};
b3 = -2 Pi/c {0, 0, 1};
reemp = {a -> 2, c -> 1};

vp[n1_, n2_, n3_] := n1 b1 + n2 b2 + n3 b3;
vps = Flatten[
        Table[vp[n1, n2, n3], {n1, 0, 5, 1}, {n2, 0, 5, 1}, {n3, 0, 5, 1}], 
      {{1, 2, 3}}] /. reemp;

VectorPlot3D[b1 /. reemp, {x, 0, 20}, {y, -50, 50}, {z, -30, 0}, VectorPoints -> vps]