The distribution of vegetation within urban zones is well understood to be important for delivery of a range of ecosystem services. While urban planners and human geographers are conversant with methodologies for describing and exploring the volumetric nature of built spaces there is less research that has developed imaginative ways of visualising the complex spatial and volumetric structure of urban vegetation from the treetops to the ground. Using waveform LiDAR data to measure the three-dimensional nature of the urban greenspace, we explore different ways of virtually, and tangibly engaging with volumetric models describing the 3D distribution of urban vegetation. Using waveform LiDAR data processed into voxels (volumetric pixels) and experimenting with a variety of creative approaches to visualise the volumetric nature of the data, we describe the development of new methods for mapping the urban green volume, using a combination of Geographic Information Systems (GIS), Minecraft, 3D printing and Computer Numerical Control (CNC) milling processes. We demonstrate how such methodologies can be used to reveal and explore the complex nature of the urban green volume. We also describe the outcome of using these models to engage diverse audiences with the volumetric data. We explain how the products could be used readily by a range of urban researchers and stakeholders: from town and city councils, to architects and ecologists.