RESEARCH TRIANGLE PARK – Imagine an iPhone that’s all display without any border. A new patent filing from Apple indicates its smartphones could be moving in that direction even as Apple mulls the possibility of renting iPhones.

Apple calls it an “ELECTRONIC DEVICE WITH WRAP AROUND DISPLAY.”

While not referring to the iPhone, Apple describes the “consumer electronic product” this way:

“[I]ncludes at least a transparent housing and a flexible display assembly enclosed within the transparent housing. In the described embodiment, the flexible display assembly is configured to present visual content at any portion of the transparent housing.”

In another part of the filing, Apple provided a bit more detail:

US PTO image

A drawing as published by the US PTO and included in Apple’s patent filing for an “electronic device with a wrap around display.”

“An electronic device having a front surface, comprising: a transparent structure having a first portion located on the front surface of the electronic device, a second portion that bends away from the first portion, and a rounded corner; and a display that displays images through the first portion of the transparent structure, the second portion of the transparent structure, and the rounded corner, wherein the display has a folded portion that conforms to the rounded corner of the transparent structure.”

Other companies have talked about smartphones that are “all screen.” But Apple appears to be serious.

Last week, Apple CEO Tim Cook said the company was looking for “more ways to allow users to pay for iPhones on a monthly basis,” Business Insider reported.

“We are cognizant that there are lots of users out there that want sort of a recurring payment like that and the receipt of new products on some sort of standard kind of basis and we are committed to make that easier to do than perhaps it is today,” he said in a conference call with analysts as reported by Business Insider.

The patent filing was made in July but only disclosed recently.

You can read the full patent filing and see more drawings online.