Mathematical imagination is an important factor in learning and solving mathematical problems by involving several types of imagination, namely sensory mathematical imagination, creative mathematical imagination and recreational mathematical imagination. This study refers to the HOTS questions as a result of the stimulus playing a role in the mathematical imagination process and based on the characteristics of the HOTS, namely maximizing the stimulus for math problems. This study aims to: 1) describe the processes and characteristics of sensory mathematical imagination in HOTS-based problem solving, 2) describe the processes and characteristics of creative mathematical imagination in HOTS-based problem solving, and 3) describe the process and characteristics of recreational mathematical imagination in solving HOTS-based problems. This research is a case study research with a qualitative approach. The main instrument in this study is the researcher himself, while other auxiliary instruments are in the form of HOTS-based test questions on the flat-sided building material at the analysis level (C4) and creation level (C6) as well as interview guidelines.

The research subjects were 5 subjects of class VIII SMP Negeri 1 Belitang II based on purposive sampling with a questionnaire. The validity of the data was obtained through data triangulation which consisted of data reduction, presentation of the data presented into a research flow chart with data information presented in a coding method consisting of open coding and axial coding, and drawing conclusions.

 Based on the results of the study, it can be concluded that: 1) the process of the emergence of sensory mathematical imagination, which begins with outlining the information in the problem, perception arises with the problem examiner, sensory stimulation (eyes, skin) to stimulate information to the brain, generate ideas based on perception, and picture illustrations to increase the ideas that arise, 2) creative mathematical imagination arises when the stimulus from HOTS questions from sensory mathematical imagination is channeled to the brain, creativity emerges the form of ideas is a form of creative mathematical imagination, there are two phases in creative mathematical imagination, namely the divergent thinking phase and the convergent thinking phase, 3) not all students can generate recreational mathematical imaginations, because recreational mathematical imaginations appear in students at the same time. at when students combine some of their creativity into a new idea.