A Locus with 25920 Linear Self-Transformations

Table of Contents

Preface
Introduction
1. The fundamental notation
2. The equation of the Burkhardt primal
3. Similarity, or equal standing, of the forty-five nodes, and of the twenty-seven pentahedra
4. The Jacobian planes of the primal
5. The k-lines of the primal
6. The Burkhardt primal is rational
7. The particular character of the forty-five nodes, and the linear transformation of the primal into itself by projection from the nodes
8. The forty Steiner threefold spaces, or primes, belonging to the primal
9. The plane common to two Steiner solids
10. The enumeration of the twenty-seven Jordan pentahedra, and of the forty-five nodes, from the nodes in pairs of polar k-lines
11. The reason for calling the Steiner tetrahedra by this name
12. The enumeration of the twenty-seven pentahedra from nine nodes of the Burkhardt primal
13. The equation of the Burkhardt primal in terms of a Steiner solid and four association primes
14. Explicit formulae for the rationalization of the Burkhardt primal
15. The equation of the Burkhardt primal referred to the prime faces of a Jordan pentahedron
16. The thirty-six double sixes of Jordan pentahedra, and the associated quadrics
17. The linear transformations of the Burkhardt primal into itself
18. Five subgroups of the group 23.34.40 transformations
19. The expression of the fundamental transformations B, C, D, S as transformations of x1,...,x6. The expression of B, C, D, S in terms of nodal projections
20. The application of the substitutions of x1,...,x6 to the twelve pentahedra {A}, {B},..., {F0}
21. The transformation of the family {A} by means of Burkhardt's transformations
22. Derivation of the Burkhardt primal from a quadratic
Appendix, note 1. The generation of desmic systems of tetrahedra in ordinary space
Appendix, note 2. On the group of substitutions of the lines of a cubic surface in ordinary space
Index of notations.

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• Front Matter (1066 KB)
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• Copyright Information Page (230 KB)
• Index (184 KB)
• Table of Contents (238 KB)