Then Simon Peter came, following him, and went into the tomb. He saw the linen cloths lying there, and the face cloth, which had been on Jesus' head, not lying with the linen cloths but folded up in a place by itself.
John 20:6-7

John appears to want to portray various disciples as being the first to perceive various aspects of Yeshua's resurrected glory. Mary Magdalene was the first to see the empty tomb and to see Yeshua, John to see the discarded linen, Peter to see the face cloth, and Thomas to touch him.

I'll leave the meaning of this pattern to you.