# Why are there 6 automorphisms for this graph?

    o
|
o---o---o---o
\         /
o       o
\     / \
o   o   \
/ \ /     o
/   o
o


(I apologise for the poor diagram unable to insert an image yet)
o represents a node and the dashed lines are arcs
My question is why are there 6 automorphisms for this graph? I can only identify 3 due to rotational symmetry.

• there are also three reflections. Your diagram does not show those well, try drawing the main triangle as a circle – Will Jagy Mar 28 at 0:39
• Oh right I see it now, thank you! – Kham Mar 28 at 0:43
• @WillJagy If you wanted to post that as an answer, I’d happily (+1) – Santana Afton Mar 28 at 2:40
• @SantanaAfton I put a picture – Will Jagy Mar 28 at 3:05