Typically, these dice are referred to by the number of faces they have: a 'd6' is a regular cubic die, pronounced 'deesix'.
Sides  Shape  Notes 

d4  tetrahedron  Each face has three numbers: they are arranged such that the top number is the same on all three visible faces. 
d6  cube  A common die. Opposite faces must add to seven. 
d8  octahedron  
d10  Irregular decahedron; see Dice/10sided dice  Each face is kiteshaped; the smallest angle of five faces point to one edge, the smallest angle of the other points to the opposite. Not a regular polyhedron. 
d12  dodecahedron  
d20  icosahedron  
d30  Each face is in the shape of a diamond.  
d100 d%  Not a polyhedron. Trade name: Zocchihedron  Usually modelled by rolling two d10, one labelled 00,10,20..90, the other normal. Examples do exist of 'true' d100's, but these are rare, and given the nickname death stars due to a passing resemblance to the Star Wars ship. Other d100s may be in the shape of a golf ball. 
Often the names of the dice appear in formulas for calculating game parameters: e.g., hit points. '6d8+10', for example, will yield a number between 16 (1×6+10) and 58 (8×6+10) with a bell curve distribution, as it means 'Roll an eightsided die six times and add ten to the total of all the rolls'. Occasionally they may be written '10×d6+20'; this means 'roll one sixsided die. Multiply it by ten and add twenty', and avoids boring repetitive dicerolling.
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