[
    {
        "id": "osp-13682",
        "type": "article-journal",
        "title": "4D Pyritohedral Symmetry",
        "author": [
            {
                "family": "Koca",
                "given": "Nazife Özdeş"
            },
            {
                "family": "Al Qanobi",
                "given": "Amal J.H."
            },
            {
                "family": "Koca",
                "given": "Mehmet"
            }
        ],
        "URL": "https://omanscience.com/ar/articles/4d-pyritohedral-symmetry",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2016
                ]
            ]
        },
        "container-title": "Sultan Qaboos University Journal for Science",
        "volume": "21",
        "issue": "2",
        "page": "150",
        "DOI": "10.24200/squjs.vol21iss2pp150-161",
        "publisher": "Sultan Qaboos University",
        "ISSN": "2308-3921",
        "abstract": "We describe an extension of the pyritohedral symmetry in 3D to 4-dimensional Euclidean space and construct the group elements of the 4D pyritohedral group of order 576 in terms of quaternions. It turns out that it is a maximal subgroup of both the rank-4 Coxeter groups W (F4) and W (H4), implying that it is a group relevant to the crystallographic as well as quasicrystallographic structures in 4-dimensions. We derive the vertices of the 24 pseudoicosahedra, 24 tetrahedra and the 96 triangular pyramids forming the facets of the pseudo snub 24-cell. It turns out that the relevant lattice is the root lattice of W (D4). The vertices of the dual polytope of the pseudo snub 24-cell consists of the union of three sets: 24-cell, another 24-cell and a new pseudo snub 24-cell. We also derive a new representation for the symmetry group of the pseudo snub 24-cell and the corresponding vertices of the polytopes."
    }
]