For Euclidean 3-space, there are 3 simple and related Goursat tetrahedra, represented by [4,3,4], [4,31,1], and [3[4]]. They can be seen inside as points on and within a cube, {4,3}.
In geometry, a Goursat tetrahedron is a tetrahedral fundamental domain of a Wythoff construction. Each tetrahedral face represents a reflection hyperplane on 3-dimensional surfaces: the 3-sphere, Euclidean 3-space, and hyperbolic 3-space. Coxeter named them after Édouard Goursat who first looked into these domains. It is an extension of the theory of Schwarz triangles for Wythoff constructions on the sphere.
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In geometry, a Goursattetrahedron is a tetrahedral fundamental domain of a Wythoff construction. Each tetrahedral face represents a reflection hyperplane...
fundamental domain of a symmetry group is an example of a Goursattetrahedron. The Goursat tetrahedra generate all the regular polyhedra (and many other...
Normale Supérieure, Sér. 3, 6, (pp. 9–102, pp. 80–81 tetrahedra), Goursattetrahedron 1951, A. C. Hurley, Finite rotation groups and crystal classes in...
vertex figure for this honeycomb is a disphenoid tetrahedron, and it is also the Goursattetrahedron (fundamental domain) for the A ~ 3 {\displaystyle...
Jordan's father originated from. Édouard Goursat, mathematician, after whom was named the Goursattetrahedron. Déodat Gratet de Dolomieu, notable geologist...
vertex figure for this honeycomb is a disphenoid tetrahedron, and it is also the Goursattetrahedron (fundamental domain) for the A ~ 3 {\displaystyle...
4] as [3,4,1+,4] : = . The doubled fundamental domain changes from a tetrahedron into a quadrilateral pyramid. Another pyramid is or , constructed as...
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