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with octahedral bounding cells, surrounding a central vertex with 24 edge-length long radii. The 4-dimensional content of a unit-edge-length 24-cell is 2, so the content of the regular octahedral pyramid is 1/12. The 24-cell tessellates 4-dimensional space as the
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with four tetrahedra wrapped around the common edge. If the height of the two apexes are the same, it can be given a higher symmetry name ∨ {4} = { } ∨ {4}, joining an edge to a perpendicular square.
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passing through the center of the 16-cell. Therefore placing two regular octahedral pyramids base to base constructs a 16-cell. The 16-cell tessellates 4-dimensional space as the
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which meet at the apex. Since an octahedron has a circumradius divided by edge length less than one, the triangular pyramids can be made with regular faces (as regular
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Exactly 24 regular octahedral pyramids will fit together around a vertex in four-dimensional space (the apex of each pyramid). This construction yields a
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along with another one more square pyramid meeting at the apex. It can also be seen in an edge-centered projection as a
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Example 4-dimensional coordinates, 6 points in first 3 coordinates for cube and 4th dimension for the apex.
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Example 4-dimensional coordinates, 8 points in first 3 coordinates for cube and 4th dimension for the apex.
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Example 4-dimensional coordinates, 2 coordinates for square, and axial points for pyramidal points.
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The graph of the octahedral pyramid is the only possible minimal counterexample to
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exists as a vertex figure in uniform polytopes of the form
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Axial-Symmetrical Edge
Facetings of Uniform Polyhedra
545:, ( ) ∨ , is a bisected octahedral pyramid. It has a
698:"20 years of Negami's planar cover conjecture"
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8:
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29:
867:
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682:"3D convex uniform polyhedra x3o4o - oct"
572:, { } ∨ , or other lower symmetry forms.
209:. Two copies can be augmented to make an
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358:The dual to the octahedral pyramid is a
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202:) by computing the appropriate height.
217:Occurrences of the octahedral pyramid
7:
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839:. You can help Knowledge (XXG) by
328:are themselves projective-planar.
205:Having all regular cells, it is a
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633:bitruncated tesseractic honeycomb
324:, that the connected graphs with
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252:The octahedral pyramid is the
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566:rectangular-pyramidal pyramid
362:, seen as a cubic base and 6
759:"Segmentotope squasc, K-4.4"
804:"Segmentotope octpy, K-4.3"
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729:10.1007/s00373-010-0934-9
570:rhombic-pyramidal pyramid
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401:Square-pyramidal pyramid
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706:Graphs and Combinatorics
577:square-pyramidal pyramid
564:can be distorted into a
562:square-pyramidal pyramid
543:square-pyramidal pyramid
394:Square-pyramidal pyramid
18:Square-pyramidal pyramid
782:Glossary for Hyperspace
629:bitruncated 5-orthoplex
696:Hliněný, Petr (2010),
258:truncated 5-orthoplex
686:1/sqrt(2) = 0.707107
211:octahedral bipyramid
891:Pyramids (geometry)
802:Klitzing, Richard.
793:Klitzing, Richard.
788:on 4 February 2007.
776:Olshevsky, George.
757:Klitzing, Richard.
680:Klitzing, Richard.
322:Negami's conjecture
227:octahedral pyramids
30:Octahedral pyramid
812:Richard Klitzing,
795:"4D Segmentotopes"
424:Polyhedral pyramid
193:triangular pyramid
191:on the base and 8
187:is bounded by one
185:octahedral pyramid
52:Polyhedral pyramid
848:
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437:∨ {4} = { } ∨ {4}
247:24-cell honeycomb
235:16-cell honeycomb
179:In 4-dimensional
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170:, regular-cells,
16:(Redirected from
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360:cubic pyramid
354:Cubic pyramid
353:
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344:( 0, 0, 0; 1)
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341:( 0, 0,±1; 0)
340:
338:( 0,±1, 0; 0)
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335:(±1, 0, 0; 0)
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841:expanding it
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786:the original
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551:tetrahedrons
549:base, and 4
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464:( )∨{3}
454:( )∨{4}
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221:The regular
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204:
200:tetrahedrons
184:
178:
151:, , order 48
67:( ) ∨ s{2,6}
65:( ) ∨ r{3,3}
886:4-polytopes
529:Properties
164:Properties
63:( ) ∨ {3,4}
880:Categories
833:4-polytope
667:References
524:, order 8
522:, order 16
510:Self-dual
231:octahedron
189:octahedron
159:, order 8
157:, order 16
155:, order 12
153:, order 24
778:"Pyramid"
715:CiteSeerX
520:, order 8
499:Vertices
124:Vertices
94:( ) ∨ {3}
181:geometry
737:2669457
441:{ } ∨
242:24-cell
223:16-cell
71:( ) ∨
745:121645
743:
735:
717:
533:convex
491:Edges
475:Faces
446:Cells
439:{ } ∨
435:( ) ∨
256:for a
183:, the
168:convex
116:Edges
105:Faces
76:Cells
69:( ) ∨
831:This
741:S2CID
701:(PDF)
507:Dual
420:Type
196:cells
132:Dual
84:{3,4}
48:Type
837:stub
631:and
575:The
560:The
541:The
368:apex
225:has
725:doi
494:13
485:{4}
480:{3}
478:12
119:18
110:{3}
108:20
882::
780:.
739:,
733:MR
731:,
723:,
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868:e
861:t
854:v
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727::
684:.
149:3
147:B
20:)
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