If Satan is such an important figure, why is there no actual physical descriptions of him?

Satan is a fallen angel, with the ability to appear in virtually any shape or image. 

Because he only resides in the spiritual world, NOT the physical.

Eph 6:12 For our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms.

He does not have a physical body because he is a former angel who is now damned to hell for eternity, though he is still free to do evil in the world by tempting people to commit sin and to avoid doing good.

There is a description of Satan, it is in The Book of Ezekiel.

The fact that the Bible does not even give him a name is the big clue. Satan and devil are adjectives describing things about him, as with adversary, accuser, serpent, roaring lion, angel of light, deceiver, man-slayer, dragon, father of lies etc. I once read a book suggesting that his rebellion against God, over who-knows-how-many-aeons-of-time, is resulting in his loss of person-hood, identity. The Bible says he was a glorious angel to begin with, but now, the evil that consumes him is so corrupting his personality that he may be losing his personal identity. Who knows?

But if you want a spiritual description of him (not to be taken literally, but using words to rightly horrify us), read Revelation chapter 12, about the red dragon. There's a great deal said about this monster in the Bible, and many adjectives applied to teach us spiritual truths about a spiritually evil entity.

Maybe she is like her mother and your head explode if you get an eye full ,

Skydaddy , mom and the gang are way to IED with a hair trigger . So far technology for said explosive feature of many skydaddy's hasn't been procured to the point of a off switch to visit mankind /. Technical term here is Skhdaddy 

You don't want to glamorize some things, as with graven images.

Why ARE there no descriptionS of him?  Because they devil can present himself as a handsome dude, and that's probably when he does most of the damage.