How can I use a different default admin menu icon for custom post type?

Question

For a particular custom post type I'm setting, I simply want to change the default icon to the wordpress pages icon (menu-icon-page).

I know I could upload my own pages icon and point to it, but can I just tell wordpress to use the default pages icon?

Here's what I'm using

register_post_type( 'intranet-pages',  // creates the custom admin panel
    array(
      'labels' => array(
       ...
        'menu_icon' => menu-icon-page,

I've tried to do different variations and can't figure it out. Thoughts? If I have to upload my own I will. Just don't want to duplicate if it's not necessary. Thanks!

UPDATE: According to this, it can't be done: How to use a WordPress' existing admin icon? At least not this simply. Does this still apply? Looks like I'll be uploading it.

UPDATE 2: See below for a more elegant solution. Simply uploading and using menu_icon => doesn't allow for the nice hover effects or the 32px icon on the edit screen.