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Concept in geometry
In geometry, a quaternionic polytope is a generalization of a polytope in real space to an analogous structure in a quaternionic module, where each real
Quaternionic_polytope
Generalization of a polytope in real space
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension
Complex_polytope
Four-dimensional number system
Quaternionic manifold – Concept in geometry Quaternionic matrix – Concept in linear algebra Quaternionic polytope – Concept in geometry Quaternionic projective
Quaternion
Four-dimensional analog of the dodecahedron
Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011). "Quaternionic representation of snub 24-cell and its dual polytope derived from E8 root system". Linear Algebra
120-cell
Regular object in four dimensional geometry
In four-dimensional geometry, the 24-cell is a convex regular 4-polytope, a four-dimensional analogue of a Platonic solid. It is named for the 24 octahedra
24-cell
(2002), No. 1, 243-259 ] Table 2, page 252 Quaternionic Construction of the W(F4) Polytopes with Their Dual Polytopes and Branching under the Subgroups W(B4)
Truncated_24-cells
Four-dimensional analog of the icosahedron
Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011). "Quaternionic representation of snub 24-cell and its dual polytope derived from E8 root system". Linear Algebra
600-cell
Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011). "Quaternionic representation of snub 24-cell and its dual polytope derived from E8 root system". Linear Algebra
Snub_24-cell
Natural number
24-cell, consisting of 24 octahedra and having 24 vertices, is a special polytope that only exists in four dimensions. The vertices of the 24-cell are the
24_(number)
63rd Johnson solid (8 faces)
Al-Ajmi, Mudhahir; Koca, Nazife Ozdes (2011). "Quaternionic representation of snub 24-cell and its dual polytope derived from E 8 {\displaystyle \mathrm {E}
Tridiminished_icosahedron
Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011). "Quaternionic representation of snub 24-cell and its dual polytope derived from E 8 {\displaystyle E_{8}} root
Dual_snub_24-cell
Hypercomplex number system
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid
Sedenion
Geometric model of the physical space
5. ISBN 978-0-19-960139-4. Morais, João Pedro; et al. (2014). Real Quaternionic Calculus Handbook. Springer Science & Business Media. pp. 1–13. ISBN 978-3-0348-0622-0
Three-dimensional_space
Finite simple group type not classified as Lie, cyclic or alternating
a type 2-3-3 triangle J2 is the group of automorphisms preserving a quaternionic structure (modulo its center). Consists of subgroups which are closely
Sporadic_group
Element of a unital algebra over the field of real numbers
{\displaystyle \mathbb {H} ^{\otimes 3}=M(4,\mathbb {H} )} yields a quaternionic matrix and its even subalgebra H ⊗ 2 ⊗ R C {\displaystyle \mathbb {H}
Hypercomplex_number
Polyhedron with 9 faces
Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011), "Quaternionic representation of snub 24-cell and its dual polytope derived from E 8 {\displaystyle E_{8}} root
Enneahedron
Generalized sphere of dimension n (mathematics)
-sphere, Lie group structure Sp(1) = SU(2). 4-sphere Homeomorphic to the quaternionic projective line, H P 1 {\displaystyle \mathbf {HP} ^{1}} . SO
N-sphere
Study of complex manifolds and several complex variables
complex structures I , J , K {\displaystyle I,J,K} which satisfy the quaternionic relations I 2 = J 2 = K 2 = I J K = − Id {\displaystyle
Complex_geometry
geometry used to describe the physical phenomena of quantum physics Quaternionic analysis Ramsey theory the study of the conditions in which order must
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Hypercomplex number system
basis with signature (− − − −) and is given in terms of the following 7 quaternionic triples (omitting the scalar identity element): ( I , j , k ) , ( i
Octonion
Completion of the usual space with "points at infinity"
naturally to the case where K is a division ring; see, for example, Quaternionic projective space. The notation PG(n, K) is sometimes used for Pn(K).
Projective_space
American mathematician (1930–2017)
of Toronto in 1966 with a dissertation title of The Theory of Uniform Polytopes and Honeycombs under the supervision of H. S. M. Coxeter.[T66] From there
Norman Johnson (mathematician)
Norman_Johnson_(mathematician)
Double cover Lie group of the special orthogonal group
group (symmetries of the hypercube, or equivalently of its dual, the cross-polytope). For point groups that reverse orientation, the situation is more complicated
Spin_group
Classification system for symmetry groups in geometry
elements can be seen in ringed nodes Coxeter-Dynkin diagram for uniform polytopes and honeycomb are related to hole nodes around the + elements, empty circles
Coxeter_notation
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