The importance of material is gradually increasing in human-computer interfaces (HCIs), especially in the design of physical objects that embody digital information. Because digital information is not comprised of physical material (Belenguer et al., in Proceedings of the Sixth International Conference on Tangible, Embedded and Embodied Interaction, ACM, New York, pp 205-212, 2012) that provides tactile feedback, advancements in HCI research involve combining physical matter with digital representations to embed materiality in immaterial beings. The emergence of new material and transmaterial (Brownell, in transmaterial: a catalog of materials that redefine our physical environment. Princeton Architectural Press, New York, 2005) indicates that material is increasingly becoming a priority in the interaction design field. We emphasize the importance of material in interaction design and discuss categories of material properties according to the characteristics of interactive systems. We divide the pre-existing materials of interaction design into three categories: tangible material, intangible material, and computational material. The relationship between tangible and computational materials has been profoundly discussed since the origin of the tangible user interface. However, intangible materials, such as air, light, and magnetism, are commonly disregarded as distinctive categorical materials in interaction design. In this paper, we argue the effectiveness of intangible materials when they are coupled with tangible and computational mediums and discuss the framework for material composition in interaction design. The concept of material composition suggests the modification of a previous perspective in interaction design, which considers that materials must have either physical or digital properties. The framework of material composition proposes various configuration dimensions that correspond to the quality of the materials used. Therefore, we manifest the framework using Inflated Roly-Poly, which is a previously developed interactive artifact, to determine the success of the reconcilement among the constituent materials and to describe the potential for investigating and resolving further implementation issues.