• Rose petal shape is determined by Mainardi-Codazzi-Peterson (MCP) incompatibility, a type of geometric frustration.
• This MCP incompatibility concentrates stress, creating the sharp cusps seen on rose petals, unlike the Gauss incompatibility seen in other plants.
• The research suggests that understanding MCP incompatibility could inspire new designs for self-morphing materials and structures.

A new study has overturned the traditional understanding of how rose petals achieve their iconic shape. For years, scientists believed that Gauss incompatibility, a phenomenon explaining the rippling edges of leaves and other petals, was responsible. However, recent research published in Science demonstrates that rose petals are shaped by a different type of geometric frustration called Mainardi-Codazzi-Peterson (MCP) incompatibility. This discovery reveals that roses use a unique mechanism to concentrate stress, resulting in the sharp, pointed cusps that distinguish them from other flowers. The findings have implications for materials science, potentially inspiring new designs for shape-morphing materials.

• What: The study reveals that rose petals' shapes are determined by a unique type of geometric frustration called Mainardi-Codazzi-Peterson (MCP) incompatibility, concentrating stress in localized areas and creating sharp cusps.
• Who: Yafei Zhang and colleagues (unspecified affiliations) conducted the research. Qinghao Cui and Lishuai Jin (Hong Kong City University) provided a related perspective. Michael Mose (Racah Institute of Physics at the Hebrew University of Jerusalem) is a co-author.
• When: The study was published in a recent issue of Science, with the articles reporting on it published around May 2, 2025.
• Where: The research involved theoretical analysis, computational modeling, and experimental fabrication of synthetic disc petals, along with the cultivation of red baccara roses.

The discovery that rose petals are shaped by MCP incompatibility, rather than the previously assumed Gauss incompatibility, represents a significant advancement in understanding morphogenesis. This finding not only explains the unique shape of rose petals but also opens up new avenues for designing self-morphing materials. The combination of theoretical analysis, computational modeling, and experimental fabrication strengthens the study's conclusions. The potential implications for robotics, aerospace, and materials science highlight the broad significance of this research.

"Identifying Mainardi-Codazzi-Peterson incompatibility as a shaping mechanism is not only an important milestone in morphogenesis research but also an inspiration for new designs of shape-morphing materials and structures."

"The rose is, to our knowledge, the only known natural system shaped by this form of incompatibility, but it may not be the only one."

The revelation that rose petals are shaped by MCP incompatibility marks a significant shift in our understanding of plant morphogenesis. This discovery not only explains the unique geometry of rose petals but also has far-reaching implications for materials science and engineering. While the study provides compelling evidence for the role of MCP incompatibility, further research is needed to explore its presence in other natural systems and fully realize its potential for bio-inspired design.