FANDOM



The icositetrachoron is a four-dimensional regular polytope composed of 24 octahedral cells, three of which join at each edge. It is also called a 24-cell because of this. Its Bowers acronym is "ico", and it can also be called a xylochoron. It is one of the three regular polychora that tile 4-dimensional space, leading to the icositetrachoric tetracomb.

Construction

One way to construct the icositetrachoron is to augment cubic pyramids onto the cells of the tesseract. If the sides of the pyramids are exactly the same edge length as the tesseract, the pyramidal cells merge into octahedra.

Another way is via the rectification of the hexadecachoron. The tetrahedral cells will rectify into octahedra, while the vertices become further octahedral cells. This can be represented as r\{3,3,4\}.

Structure and Sections

Structure

The icositetrachoron is composed of octahedra joining six to a vertex. Seen from a cell, we first have one, then the eight joining to it. The next layer is six octahedra sharing only a vertex with the top, then another eight, and finally the opposite cell.

Subfacets

Hypervolumes

See also

\{3,4,2\} \{3,4,3\} \{3,4,4\}
Octahedral dichoron Icositetrachoron Order-4 octahedral honeycomb
\{2,4,3\} \{3,4,3\} \{4,4,3\}
Cubic hosochoron Icositetrachoron Order-3 square tiling honeycomb
Regular
t_0 \{3,4,3\}
Rectified
t_1 \{3,4,3\}
Birectified
t_2 \{3,4,3\}
Trirectified
t_3 \{3,4,3\}
Truncated
t_{0,1} \{3,4,3\}
Bitruncated
t_{1,2} \{3,4,3\}
Tritruncated
t_{2,3} \{3,4,3\}
Icositetrachoron Rectified icositetrachoron Rectified icositetrachoron Icositetrachoron Truncated icositetrachoron Bitruncated icositetrachoron Truncated icositetrachoron
Cantellated
t_{0,2} \{3,4,3\}
Bicantellated
t_{1,3} \{3,4,3\}
Cantitruncated
t_{0,1,2} \{3,4,3\}
Bicantitruncated
t_{1,2,3} \{3,4,3\}
Runcinated
t_{0,3} \{3,4,3\}
Runcicantellated
t_{0,2,3} \{3,4,3\}
Runcitruncated
t_{0,1,3} \{3,4,3\}
Runcicantitruncated
t_{0,1,2,3} \{3,4,3\}
Cantellated pentachoron Cantellated icositetrachoron Cantitruncated icositetrachoron Cantitruncated icositetrachoron Runcinated icositetrachoron Runcitruncated icositetrachoron Runcitruncated icositetrachoron Omnitruncated icositetrachoron
Regular
t_0 \{4,3,3\}
Rectified
t_1 \{4,3,3\}
Birectified
t_2 \{4,3,3\}
Trirectified
t_3 \{4,3,3\}
Truncated
t_{0,1} \{4,3,3\}
Bitruncated
t_{1,2} \{4,3,3\}
Tritruncated
t_{2,3} \{4,3,3\}
Tesseract Rectified tesseract Icositetrachoron Hexadecachoron Truncated tesseract Bitruncated tesseract Truncated hexadecachoron
Cantellated
t_{0,2} \{4,3,3\}
Bicantellated
t_{1,3} \{4,3,3\}
Cantitruncated
t_{0,1,2} \{4,3,3\}
Bicantitruncated
t_{1,2,3} \{4,3,3\}
Runcinated
t_{0,3} \{4,3,3\}
Runcicantellated
t_{0,2,3} \{4,3,3\}
Runcitruncated
t_{0,1,3} \{4,3,3\}
Runcicantitruncated
t_{0,1,2,3} \{4,3,3\}
Cantellated tesseract Rectified icositetrachoron Cantitruncated tesseract Truncated icositetrachoron Runcinated tesseract Runcitruncated hexadecachoron Runcitruncated tesseract Omnitruncated tesseract
Regular
t_0 \{3,3,b3\}
Rectified
t_1 \{3,3,b3\}
Birectified
t_2 \{3,3,b3\}
Trirectified
t_3 \{3,3,b3\}
Truncated
t_{0,1} \{3,3,b3\}
Bitruncated
t_{1,2} \{3,3,b3\}
Tritruncated
t_{2,3} \{3,3,b3\}
Hexadecachoron Icositetrachoron Hexadecachoron Hexadecachoron Truncated Hexadecachoron Truncated Hexadecachoron Rectified tesseract
Cantellated
t_{0,2} \{3,3,b3\}
Bicantellated
t_{1,3} \{3,3,b3\}
Cantitruncated
t_{0,1,2} \{3,3,b3\}
Bicantitruncated
t_{1,2,3} \{3,3,b3\}
Runcinated
t_{0,3} \{3,3,b3\}
Runcicantellated
t_{0,2,3} \{3,3,b3\}
Runcitruncated
t_{0,1,3} \{3,3,b3\}
Runcicantitruncated
t_{0,1,2,3} \{3,3,b3\}
Rectified tesseract Truncated hexadecachoron Bitruncated tesseract Bitruncated tesseract Rectified tesseract Rectified icositetrachoron Bitruncated tesseract Truncated icositetrachoron
t_1 \{2,3,4\} t_1 \{3,3,4\} t_1 \{4,3,4\} t_1 \{5,3,4\} t_1 \{6,3,4\}
Rectified Octahedral hosochoron Icositetrachoron Rectified cubic honeycomb Rectified order-4 dodecahedral honeycomb Rectified order-4 Hexagonal tiling honeycomb
t_1 \{3,3,2\} t_1 \{3,3,3\} t_1 \{3,3,4\} t_1 \{3,3,5\} t_1 \{3,3,6\}
Rectified tetrahedral dichoron Rectified pentachoron Icositetrachoron Rectified hexacosichoron Rectified order-6 tetrahedral honeycomb

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.