<![CDATA[The difficulty of learning to build polyhedron for middle students makes experts lecturers collaboratively create learning trajectories through the Lesson Study for Learning Community (LSLC). This study aims to produce a learning trajectory that can assist students in learning polyhedron using collaborative learning through LSLC. The research method used was design research with the first stage, preparing for experiment, experimental design, and retrospective analysis. This learning approach uses collaborative LSLC is used in the process of making teaching materials and along with research methods. This study involved 47 lecturers and 24 mathematics education students. Data collection was carried out through observing student activities, recording video events in class, collecting student work results, and student test results. The collected data were then analyzed retrospectively with the results showing that collaborative and LSLC used in the acquired learning paths can help students in learning flat-sided shapes. The learning trajectory includes (1) students can collaboratively understand the surface area of the cube (2) collaboratively, students can understand the space diagonal of a block. With the existence of LSLC, researchers can form learning communities with research subjects, collaborate in making learning designs and teaching materials, and produce multilevel effective learning through sharing tasks and jumping tasks ]]>
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