page_title: Truncated tesseract
section_title: Centered on octahedron
hierarchical_section_title: Truncated tesseract / Truncated 16-cell / Projections / Centered on octahedron
caption_attribution_description: English: Parallel projection of the truncated 16-cell into 3D, centered on an octahedral cell, with hidden cells culled.
context_page_description: In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract.
  There are three truncations, including a bitruncation, and a tritruncation, which creates the truncated 16-cell.
context_section_description: The octahedron-first parallel projection of the truncated 16-cell into 3-dimensional space has the following structure:
  The projection envelope is a truncated octahedron.
  The 6 square faces of the envelope are the images of 6 of the octahedral cells.
  An octahedron lies at the center of the envelope, joined to the center of the 6 square faces by 6 edges. This is the image of the other 2 octahedral cells.
  The remaining space between the envelope and the central octahedron is filled by 8 truncated tetrahedra (distorted by projection). These are the images of the 16 truncated tetrahedral cells, a pair of cells to each image.
  This layout of cells in projection is analogous to the layout of faces in the projection of the truncated octahedron into 2-dimensional space. Hence, the truncated 16-cell may be thought of as the 4-dimensional analogue of the truncated octahedron.
caption: Octahedron-first parallel projection into 3 dimensions, with octahedral cells highlighted