I like the idea ... Think it's cute...
Not sure how you will pass the graphic standards here, they seem a little high to me...
Maybe display them as if they are rolled out on a table with poker chips and snacks around it ..
A few suggestions:
Instead of drawing lines for the connections of the dice -
just add in the rules what the connections are and make them a math equation..
Example:
- Click image to enlarge.

Dice are broken up into sectors:
(BL) Bottom Left (BR) Bottom Right (BC) Bottom Center
(TL) Top Left (TR) Top Right (TC) Top Center
(C) center
Dot's on a Die can attack any adjacent dot to it on the same Die
"This is all ready displayed by your green lines - but I feel with this
one statement you can clear the board of your green lines.
All dots on all dice can attack (one way) against 1 for they are all divisible by 1.
But one can only attack 3 or 5 since they are the only one's with a center dot.
(Red dot's are connected)
All other dice can only attack any dot on another die that is in it's same sector and is divisible or a multiple of that die.
example:
2 has 2 dots
the (TR) dot on 2 can attack the (TR) dot on 4 or 6 and vise versa
the (BL) dot on 2 can attack the (BL) dot on 4 or 6 and vise versa
Connections:
1 to 3 and 5
2 to 1, 4 and 6
3 to 1 and 6
4 to 1 and 2
5 to 1
6 to 1, 2 and 3
5 is an island like austrillia with the Die#1 as a secure doorway (except die#1 is not that secure for it can be attacked by all)
Suggestion on Bonuses:
Die 1 if completely controlled +1 (or since 1 die is so powerful location make it a -3 for controlling it)
Die 2 if completely controlled +5
Die 3 if completely controlled +4
Die 4 if completely controlled +3
Die 5 if completely controlled +2
Die 6 if completely controlled +6
Then maybe an extra bonus for players that control any 2 dice that equal 7
1 and 6 you get +3
2 and 5 you get +3
3 and 4 you get +3
((Even though 5 has more dot's to capture to be able to control then say die 2; you'll see 5 has the least bonus and this is because it's the only die that is it's own island and is easiest to protect.))
just some ideas for your cute concept...
Visual idea of the connections .. Not showing the one way connection they all have to the die#1
- Click image to enlarge.

- Click image to enlarge.
