Mathematicians created an ‘impossible’ shape that shouldn’t exist

image via New Scientist

April 14, 2026, 10:00 AM

• •Impossible objects appear realistic but cannot exist in reality.
• •The new shape is based on a Klein bottle with a multilevel staircase.
• •The order of loops affects the outcome, creating nonabelian properties.
• •This is the first visual paradox with nonabelian properties.

Mathematicians Robert Ghrist and Zoe Cooperband have created a new impossible object, building upon the concept of visual paradoxes. This shape is a continuous multilevel staircase modeled on a Klein bottle, where a bug's orientation flips when crossing a vertical edge. The shape allows for different outcomes depending on the order in which a bug navigates horizontal and vertical loops, a property known as nonabelian. This is the first time such a property has been observed in a visual paradox.

Read original article