With the inspiration of your replies, I found a way of doing this quickly and precisely, which I would like to share.
Step 1: Axonometric grid
Document Properties //
Grid and create a new axonometric grid. Spacing Y x Major grid line every should represent the side length of your desired triangle.
I want my triangles to have a side length of 18 mm so I use these settings
Step 2: Triangle
Using the Bezier tool and Snap-to-Grid, create a triangle along the major grid lines
Step 3: Spacings
Now we define the spacings between the triangles: set the triangle stroke width to the spacing you want between your triangles.
I want my spacings to be 4 mm so this is what I set the stroke to.
Step 4: Set the rotation point
In the snap toolset, disable
Snap to Grid and enable
Snap to bounding-boxes
Snap to bounding-box-corner
Snap to misc. points
Snap to object rotation center
Switch to the select tool and click the triangle twice so that the rotation tool appears. Drag the rotation center to the right lower bounding box-point of the triangle
Step 5: Hexagon
Now we duplicate the triangle to create a hexagon.
Ctrl + D to duplicate the triangle and then rotate it by 30 ° (holding
Ctrl) so it snaps to the previous one. Repeat this 5 to receive a hexagon
Select all 6 triangles and create an object group (
Ctrl + G).
Step 6: Tiled Clones - Part One
Here begins the mathematical part: Go to
Create Tiled Clones ... and create a Simple translation with 2 rows and one column.
Shift tab, we have to specify how much the cloned hexagon in the second row has to be moved to snug to the right lower edge of the original hexagon.
To illustrate that, first leave all shift values at zero and hit
Create. The new hexagon is right below the first one. We want it to be shifted 50 % to the right so we enter 50 % in
We also want the cloned hexagon to go upwards. For mathematical reasons that go beyond this guide (maybe somebody likes to leave a comment on that?), it can be shown that the correct value for the
Shift Y is -25 %
Step 7: Tiled Clones - Part Two
Select both Hexagons and create a new object group.
Now we create the final grid. Go to
Create Tiled Clones again and specify your desired number of rows and columns.
Shift tab we have to specify the correct values again. As the hexagon group is "three triangles wide" and we want to snug every new clone in the free space of the previous one,
Per column has to be - 1/3. Inkscape understands math, so you can enter
-1/3 * 100 in this field.
Per Row is more difficult. Like in Step 6, we want it to be 25 % of one hexagon. However, we have two hexagons now, so we have to adapt for that.
As we moved the cloned hexagon up by 25 % in Step 6, we know, that the hexagon group has a height of 175 % of one hexagon. We therefore can calculate that each row has to be moved 25 % / 175 % which doesn't give a nice number. However, as stated, Inkscape understands math. So we enter
-25 / 175 * 100 in
Make sure all other shift values are set to zero
Step 8: Remove Stroke
Finally we can remove the stroke that we just used as a guidance.
Select all triangles and set the Stroke to no paint
You are finished.
So far, so good. As I want to laser cut the mesh out of plastic, I prefer to have the corners rounded. To achieve that, I wanted to use
Path Effects //
Corners (Fillet/Chamfer). However, this tool behaves weird with discontiguous pathes. Maybe this is some kind of bug or the tool is not designed for discontiguous pathes.
In order to still have round corners, I would now use the method user287001 mentions and put a rounded triangle on top of a "pointy" rectangle right in the beginning.