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Look Inside A Locus with 25920 Linear Self-Transformations

A Locus with 25920 Linear Self-Transformations


Part of Cambridge Tracts in Mathematics

  • Date Published: March 2015
  • availability: Available
  • format: Paperback
  • isbn: 9781107493711

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About the Authors
  • Originally published in 1946 as number thirty-nine in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding linear groups. Appendices are also included. This book will be of value to anyone with an interest in linear groups and the history of mathematics.

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    Product details

    • Date Published: March 2015
    • format: Paperback
    • isbn: 9781107493711
    • length: 120 pages
    • dimensions: 220 x 140 x 10 mm
    • weight: 0.17kg
    • availability: Available
  • Table of Contents

    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.

  • Author

    H. F. Baker

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