Mesh only displayed in wireframe in edit mode

I have this character, rigged, with an armature in Blender 2.79.

I want to edit some vertices and when entering edit mode, the character is still displayed in the animation frame it was left to, but the t-pose for editing is only displayed in wireframe mode.

  • I’m not in wireframe mode
  • The maximum draw type is “Textured”
  • Don’t have Hidden Wire activated

Any idea?