<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-2320</article-id>
      <title-group>
        <article-title>Special triad of tetrahedrons and s-transformation in a three-dimensional projective space</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Panda</surname>
            <given-names>Golak Bihari</given-names>
          </name>
          <aff>Department of Mathematics, Siksha ‘O’ Anusandhan (Deemed to be University), Institute of Technical Education and Research, Bhubaneswar, Odisha, 751030, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Misra</surname>
            <given-names>Saroj Kanta</given-names>
          </name>
          <aff>Department of Basic Sciences &amp; Humanities, Silicon Institute of Technology, Bhubaneswar, Odisha, 751024, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>6</issue>
      <fpage>1849</fpage>
      <lpage>1859</lpage>
      <pub-date date-type="pub">
        <day>30</day>
        <month>06</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>Given a pair of perspective tetrahedron (A) and (B) where the vertex Bi is on the opposite face of Ai the center and plane of perspectivity are called the pole and polar of each other respectively for the reference tetrahedron (A). Konully studied a pair of mutually self polar tetrahedrons and Sanyal [9] studied the polar tetrahedrons (C) of (B) for some reference (A). Misra and Sanyal [7] studied a conjugate pair where each of the pair is the polar tetrahedron of the other for (A). In the present study a triad of double perspective tetrahedrons is obtained which under special condition form a special triad where every pair is a conjugate pair for the third. Using a transformation called s-transformation a family of special triad is obtained, which is fixed for a fixed reference (A) and a point P not on the face of (A).  The different centers of perspectivities of the double perspective pairs of this family form desmic systems.</p>
      </abstract>
      <kwd-group>
        <kwd>Homogeneous coordinates</kwd>
        <kwd>Perspective tetrahedrons</kwd>
        <kwd>Pole and polar</kwd>
        <kwd>Cross-ratio</kwd>
        <kwd>Conjugate tetrahedrons</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
