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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
Four-dimensional number system
Quaternionic manifold – Concept in geometry Quaternionic matrix – Concept in linear algebra Quaternionic polytope – Concept in geometry Quaternionic projective
Quaternion
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
(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 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
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
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
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)
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
Hypercomplex number system
Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid
Sedenion
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
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
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
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
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
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
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
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. From there,
Norman Johnson (mathematician)
Norman_Johnson_(mathematician)
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
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
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
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
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
QUATERNIONIC POLYTOPE
QUATERNIONIC POLYTOPE
Biblical
a guard of four soldiers,...and delivered him to four quaternions of soldiers to guard him...
QUATERNIONIC POLYTOPE
QUATERNIONIC POLYTOPE
Girl/Female
Tamil
Group lets of stars
Surname or Lastname
English
English : occupational name for a moneylender or minter or a nickname for a rich man, from Old French ducat (Italian ducato), name of a gold coin. This was spelled duket in Middle English; Ducat is a ‘restored’ form. It has been confused with Duckett.Scottish : probably a variant of Duguid.French : patronymic from the nickname Cat, from a dialect variant of chat ‘cat’.Variant spelling of German and Jewish Dukat, cognate with 1.
Girl/Female
Muslim
Happy, Sweet
Boy/Male
English American French
Spear strength.
Boy/Male
Tamil
Gangadhara | கஂகாதரா
Lord of river Ganga, Lord Shiva
Male
Hebrew
(יׄ×ש×ִיָּה) Hebrew name YOSHIYAH means "whom Jehovah heals." In the bible, this is the name of the sixteenth king of Judah. Josiah is the Anglicized form.
Boy/Male
Hindu, Indian, Marathi
Wearing Golden Ornaments
Boy/Male
Muslim
Skillful. Intelligent.
Girl/Female
Hindu, Indian, Tamil
Realy Smart
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Flower
QUATERNIONIC POLYTOPE
QUATERNIONIC POLYTOPE
QUATERNIONIC POLYTOPE
QUATERNIONIC POLYTOPE
QUATERNIONIC POLYTOPE
n.
The turning factor of a quaternion.
n.
A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
n.
The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
v. t.
To divide into quaternions, files, or companies.
n.
The number four.
n.
The number four; a collection of four things; a quaternion.
n.
In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.
n.
A word of four syllables; a quadrisyllable.