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around every vertex. Placing 8 cubic pyramids on the cubic bounding cells of a tesseract is Gosset's construction of the 24-cell. Thus the 24-cell is constructed from exactly 16 cubic pyramids. The 24-cell tessellates 4-dimensional space as the
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A cubic pyramid of height zero can be seen as a cube divided into 6 square pyramids along with the center point. These square pyramid-filled cubes can tessellate three-dimensional space as a dual of the
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which meet at the apex. Since a cube has a circumradius divided by edge length less than one, the square pyramids can be made with regular faces by computing the appropriate height.
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Exactly 8 regular cubic pyramids will fit together around a vertex in four-dimensional space (the apex of each pyramid). This construction yields a
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with 8 cubical bounding cells, surrounding a central vertex with 16 edge-length long radii. The tesseract tessellates 4-dimensional space as the
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234:. The 4-dimensional content of a unit-edge-length tesseract is 1, so the content of the regular cubic pyramid is 1/8.
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onto the faces of a cube, and folded along the squares where the pyramids meet the cube.
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The cubic pyramid can be folded from a three-dimensional
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Axial-Symmetrical Edge
Facetings of Uniform Polyhedra
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342:(Third ed.). New York: Dover. p. 150.
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324:"3D convex uniform polyhedra o3o4x - cube"
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253:The dual to the cubic pyramid is an
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222:Related polytopes and honeycombs
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215:3D projection while rotating
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383:"Segmentotope cubpy, K-4.26"
297:in the form of a non-convex
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280:truncated cubic honeycomb
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338:Coxeter, H.S.M. (1973).
363:Glossary for Hyperspace
284:hexakis cubic honeycomb
301:, obtained by gluing
232:tesseractic honeycomb
328:sqrt(3)/2 = 0.866025
265:meeting at an apex.
261:base, and 8 regular
468:Pyramids (geometry)
381:Klitzing, Richard.
374:Klitzing, Richard.
369:on 4 February 2007.
357:Olshevsky, George.
322:Klitzing, Richard.
299:tetrakis hexahedron
389:Richard Klitzing,
376:"4D Segmentotopes"
255:octahedral pyramid
191:on the base and 6
187:is bounded by one
129:Octahedral pyramid
41:Polyhedral pyramid
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340:Regular Polytopes
248:24-cell honeycomb
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179:In 4-dimensional
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48:Schläfli symbols
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237:The regular
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144:, , order 48
463:4-polytopes
288:pyramidille
282:, called a
153:Properties
52:( ) ∨ {4,3}
457:Categories
410:4-polytope
309:References
263:tetrahedra
259:octahedral
148:, order 8
146:, order 16
359:"Pyramid"
228:tesseract
117:Vertices
79:( ) ∨ {4}
181:geometry
239:24-cell
56:( ) ∨
202:Images
183:, the
157:convex
109:Edges
90:Faces
61:Cells
54:( ) ∨
408:This
286:, or
196:cells
125:Dual
69:{4,3}
37:Type
414:stub
241:has
189:cube
295:net
165:Net
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103:{4}
98:{3}
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