SL := false;
id := "gl3";
matrank := 3;

standardorder := [
	      [1, 0, 0],
	      [0, 1, 0],
	      [0, 0, 1],
	      [1, 1, 0],
	      [0, 1, 1],
	      [1, 1, 1]
	      ];


V := [ PowerSequence(PowerStructure(Rec)) |
    [ PowerStructure(Rec) |
        rec<cellrec | 
            vertices := \[ 1, 2, 3 ],
            stabilizer := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ 0, 0, -1, 0, 1, 0, -1, 0, 0 ]),
                    Matrix(3, 3, \[ -1, 0, 0, 0, 0, -1, 0, -1, 0 ]),
                    DiagonalMatrix([1, 1, -1])
                        /* order = 48 = 2^4 * 3 */ > |
                \[ 0, 0, -1, 0, 1, 0, -1, 0, 0 ],

                \[ 1, 0, 0, 0, -1, 0, 0, 0, 1 ],

                \[ 0, -1, 0, 0, 0, 1, -1, 0, 0 ],

                \[ -1, 0, 0, 0, 1, 0, 0, 0, -1 ],

                \[ 0, -1, 0, -1, 0, 0, 0, 0, 1 ],

                \[ 1, 0, 0, 0, 0, -1, 0, 1, 0 ],

                \[ 1, 0, 0, 0, 0, -1, 0, -1, 0 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ 0, 1, 0, -1, 0, 0, 0, 0, -1 ],

                \[ 0, 0, -1, 0, -1, 0, -1, 0, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 0, 0, 1, 1, 0, 0, 0, -1, 0 ],

                \[ 0, 0, 1, 0, 1, 0, 1, 0, 0 ],

                \[ 0, -1, 0, 0, 0, -1, 1, 0, 0 ],

                \[ -1, 0, 0, 0, 0, -1, 0, 1, 0 ],

                \[ 0, 0, -1, 1, 0, 0, 0, 1, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, 0, 0, 1, 0, -1, 0 ],

                \[ 0, 0, -1, -1, 0, 0, 0, 1, 0 ],

                \[ 0, -1, 0, -1, 0, 0, 0, 0, -1 ],

                \[ 0, 0, 1, 0, 1, 0, -1, 0, 0 ],

                \[ 0, 1, 0, 0, 0, -1, 1, 0, 0 ],

                \[ 0, 1, 0, 0, 0, -1, -1, 0, 0 ],

                \[ 0, -1, 0, 0, 0, 1, 1, 0, 0 ],

                \[ 0, 0, -1, 0, 1, 0, 1, 0, 0 ],

                \[ 0, 0, -1, 0, -1, 0, 1, 0, 0 ],

                \[ 0, 0, 1, 0, -1, 0, -1, 0, 0 ],

                \[ 0, 0, 1, -1, 0, 0, 0, 1, 0 ],

                \[ 0, 0, 1, -1, 0, 0, 0, -1, 0 ],

                \[ 0, 0, -1, -1, 0, 0, 0, -1, 0 ],

                \[ 0, 1, 0, -1, 0, 0, 0, 0, 1 ],

                \[ 0, 1, 0, 0, 0, 1, -1, 0, 0 ],

                \[ -1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, 0, 0, -1, 0, -1, 0 ],

                \[ 0, 1, 0, 1, 0, 0, 0, 0, -1 ],

                \[ 0, 1, 0, 1, 0, 0, 0, 0, 1 ],

                \[ 0, -1, 0, 1, 0, 0, 0, 0, 1 ],

                \[ 0, 0, 1, 1, 0, 0, 0, 1, 0 ],

                \[ -1, 0, 0, 0, 0, 1, 0, 1, 0 ],

                \[ 0, 0, -1, 1, 0, 0, 0, -1, 0 ],

                \[ 1, 0, 0, 0, 0, 1, 0, 1, 0 ],

                \[ 0, 0, 1, 0, -1, 0, 1, 0, 0 ],

                \[ 0, -1, 0, 1, 0, 0, 0, 0, -1 ],

                \[ 0, 1, 0, 0, 0, 1, 1, 0, 0 ],

                \[ 1, 0, 0, 0, 0, 1, 0, -1, 0 ],

                \[ 0, -1, 0, 0, 0, -1, -1, 0, 0 ]
            ],
            stabilizerplus := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ 0, 0, -1, 0, 1, 0, -1, 0, 0 ]),
                    Matrix(3, 3, \[ -1, 0, 0, 0, 0, -1, 0, -1, 0 ]),
                    DiagonalMatrix([1, 1, -1])
                        /* order = 48 = 2^4 * 3 */ > |
                \[ 1, 0, 0, 0, -1, 0, 0, 0, 1 ],

                \[ 0, -1, 0, 0, 0, 1, -1, 0, 0 ],

                \[ -1, 0, 0, 0, 1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 0, 0, 1, 1, 0, 0, 0, -1, 0 ],

                \[ 0, -1, 0, 0, 0, -1, 1, 0, 0 ],

                \[ 0, 0, -1, 1, 0, 0, 0, 1, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, 1 ],

                \[ 0, 0, -1, -1, 0, 0, 0, 1, 0 ],

                \[ 0, 1, 0, 0, 0, -1, 1, 0, 0 ],

                \[ 0, 1, 0, 0, 0, -1, -1, 0, 0 ],

                \[ 0, -1, 0, 0, 0, 1, 1, 0, 0 ],

                \[ 0, 0, 1, -1, 0, 0, 0, 1, 0 ],

                \[ 0, 0, 1, -1, 0, 0, 0, -1, 0 ],

                \[ 0, 0, -1, -1, 0, 0, 0, -1, 0 ],

                \[ 0, 1, 0, 0, 0, 1, -1, 0, 0 ],

                \[ -1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ 0, 0, 1, 1, 0, 0, 0, 1, 0 ],

                \[ 0, 0, -1, 1, 0, 0, 0, -1, 0 ],

                \[ 0, 1, 0, 0, 0, 1, 1, 0, 0 ],

                \[ 0, -1, 0, 0, 0, -1, -1, 0, 0 ]
            ],
            facetdata := [],
            barycenter := \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],
            facets := [ PowerSequence(IntegerRing()) | ]>
    ],
    [ PowerStructure(Rec) |
        rec<cellrec | 
            vertices := \[ 1, 2, 3, 4 ],
            stabilizer := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ 0, 1, 0, 1, 0, 0, 0, 0, 1 ]),
                    ScalarMatrix(3, -1),
                    Matrix(3, 3, \[ -1, 0, 0, -1, 1, 0, 0, 0, 1 ]),
                    DiagonalMatrix([-1, -1, 1])
                        /* order = 24 = 2^3 * 3 */ > |
                \[ 1, -1, 0, 1, 0, 0, 0, 0, 1 ],

                \[ 0, 1, 0, 1, 0, 0, 0, 0, 1 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 1, 0, -1, 0, 0, 0, 0, -1 ],

                \[ 0, -1, 0, 1, -1, 0, 0, 0, -1 ],

                \[ -1, 1, 0, 0, 1, 0, 0, 0, -1 ],

                \[ 0, -1, 0, -1, 0, 0, 0, 0, -1 ],

                \[ 0, 1, 0, -1, 1, 0, 0, 0, -1 ],

                \[ 1, 0, 0, 1, -1, 0, 0, 0, 1 ],

                \[ 1, -1, 0, 0, -1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, -1, 1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, -1, 1, 0, 0, 0, -1 ],

                \[ 1, -1, 0, 0, -1, 0, 0, 0, -1 ],

                \[ 1, 0, 0, 1, -1, 0, 0, 0, -1 ],

                \[ 0, 1, 0, -1, 1, 0, 0, 0, 1 ],

                \[ -1, 1, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 0, -1, 0, -1, 0, 0, 0, 0, 1 ],

                \[ 0, -1, 0, 1, -1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, 1 ],

                \[ -1, 1, 0, -1, 0, 0, 0, 0, 1 ],

                \[ 1, -1, 0, 1, 0, 0, 0, 0, -1 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, -1 ],

                \[ 0, 1, 0, 1, 0, 0, 0, 0, -1 ]
            ],
            stabilizerplus := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ 0, 1, 0, 1, 0, 0, 0, 0, 1 ]),
                    ScalarMatrix(3, -1),
                    Matrix(3, 3, \[ -1, 0, 0, -1, 1, 0, 0, 0, 1 ]),
                    DiagonalMatrix([-1, -1, 1])
                        /* order = 24 = 2^3 * 3 */ > |
                \[ 1, -1, 0, 1, 0, 0, 0, 0, 1 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 1, 0, -1, 0, 0, 0, 0, -1 ],

                \[ 0, -1, 0, 1, -1, 0, 0, 0, -1 ],

                \[ 0, 1, 0, -1, 1, 0, 0, 0, -1 ],

                \[ 0, 1, 0, -1, 1, 0, 0, 0, 1 ],

                \[ 0, -1, 0, 1, -1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, 1 ],

                \[ -1, 1, 0, -1, 0, 0, 0, 0, 1 ],

                \[ 1, -1, 0, 1, 0, 0, 0, 0, -1 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, -1 ]
            ],
            facetdata := [ PowerStructure(Rec) |
                rec<cellrec | 
                    vertices := \[ 1, 2, 3 ],
                    mover := \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],
                    type := 1,
                    orientationstd := 1>,
                rec<cellrec | 
                    vertices := \[ 2, 3, 4 ],
                    mover := \[ 0, 1, 0, -1, 1, 0, 0, 0, 1 ],
                    type := 1,
                    orientationstd := 1>,
                rec<cellrec | 
                    vertices := \[ 1, 3, 4 ],
                    mover := \[ 1, 1, 0, 0, 1, 0, 0, 0, 1 ],
                    type := 1,
                    orientationstd := -1>
            ],
            barycenter := \[ 2, 1, 0, 1, 2, 0, 0, 0, 1 ],
            facets := [ PowerSequence(IntegerRing()) |
                \[ 1, 2, 3 ],
                \[ 2, 3, 4 ],
                \[ 1, 3, 4 ]
            ]>,
        rec<cellrec | 
            vertices := \[ 1, 3, 4, 5 ],
            stabilizer := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ -1, 0, 0, 0, -1, 1, 0, 0, 1 ]),
                    Matrix(3, 3, \[ -1, 0, 0, -1, 1, 0, 0, 0, 1 ]),
                    ScalarMatrix(3, -1),
                    Matrix(3, 3, \[ 0, 0, 1, 1, -1, 1, 1, 0, 0 ]),
                    Matrix(3, 3, \[ 0, -1, 1, 0, -1, 0, 1, -1, 0 ])
                        /* order = 48 = 2^4 * 3 */ > |
                \[ 0, 1, -1, -1, 1, -1, -1, 1, 0 ],

                \[ -1, 1, 0, 0, 0, 1, 0, -1, 1 ],

                \[ -1, 0, 0, -1, 1, -1, 0, 0, -1 ],

                \[ 0, 0, 1, 0, -1, 1, -1, 0, 0 ],

                \[ 0, 0, -1, -1, 1, -1, -1, 0, 0 ],

                \[ 1, 0, 0, 1, -1, 1, 0, 0, 1 ],

                \[ -1, 1, 0, -1, 1, -1, 0, 1, -1 ],

                \[ 0, 1, 0, 0, 0, 1, 1, -1, 1 ],

                \[ 0, 1, 0, 0, 1, -1, -1, 1, -1 ],

                \[ 0, 1, 0, 1, 0, 0, 1, -1, 1 ],

                \[ -1, 0, 0, -1, 1, 0, 0, 0, 1 ],

                \[ 1, -1, 0, 0, 0, -1, 0, 1, -1 ],

                \[ 1, -1, 1, 0, 0, 1, 0, 1, 0 ],

                \[ 0, 1, -1, 0, 1, 0, -1, 1, 0 ],

                \[ 1, -1, 1, 1, 0, 0, 0, 1, 0 ],

                \[ -1, 1, -1, -1, 1, 0, 0, 1, 0 ],

                \[ 0, 0, -1, 0, -1, 0, -1, 0, 0 ],

                \[ 0, -1, 0, 1, -1, 0, 1, -1, 1 ],

                \[ 1, 0, 0, 0, 1, -1, 0, 0, -1 ],

                \[ 1, 0, 0, 1, -1, 0, 0, 0, -1 ],

                \[ 0, -1, 0, 0, -1, 1, 1, -1, 1 ],

                \[ 1, -1, 0, 1, 0, 0, 0, 1, -1 ],

                \[ -1, 1, 0, -1, 0, 0, 0, -1, 1 ],

                \[ 0, -1, 1, 0, -1, 0, 1, -1, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 0, -1, 1, 1, -1, 1, 1, -1, 0 ],

                \[ 0, 1, -1, 0, 0, -1, 1, -1, 0 ],

                \[ 0, 1, 0, -1, 1, 0, -1, 1, -1 ],

                \[ -1, 0, 0, 0, -1, 1, 0, 0, 1 ],

                \[ 0, 0, -1, 1, -1, 0, 1, 0, 0 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ 0, 0, -1, 0, 1, -1, 1, 0, 0 ],

                \[ 0, 0, 1, 1, -1, 1, 1, 0, 0 ],

                \[ 0, -1, 1, -1, 0, 0, -1, 1, 0 ],

                \[ -1, 1, -1, 0, 1, -1, 0, 1, 0 ],

                \[ -1, 1, -1, -1, 0, 0, 0, -1, 0 ],

                \[ 1, -1, 0, 0, -1, 0, 0, -1, 1 ],

                \[ 1, -1, 0, 1, -1, 1, 0, -1, 1 ],

                \[ 0, -1, 0, 0, 0, -1, -1, 1, -1 ],

                \[ 0, 0, 1, -1, 1, 0, -1, 0, 0 ],

                \[ -1, 1, -1, 0, 0, -1, 0, -1, 0 ],

                \[ 0, -1, 1, 0, 0, 1, -1, 1, 0 ],

                \[ 1, -1, 1, 1, -1, 0, 0, -1, 0 ],

                \[ 1, -1, 1, 0, -1, 1, 0, -1, 0 ],

                \[ 0, -1, 0, -1, 0, 0, -1, 1, -1 ],

                \[ 0, 0, 1, 0, 1, 0, 1, 0, 0 ],

                \[ -1, 1, 0, 0, 1, 0, 0, 1, -1 ],

                \[ 0, 1, -1, 1, 0, 0, 1, -1, 0 ]
            ],
            stabilizerplus := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ -1, 0, 0, 0, -1, 1, 0, 0, 1 ]),
                    Matrix(3, 3, \[ -1, 0, 0, -1, 1, 0, 0, 0, 1 ]),
                    ScalarMatrix(3, -1),
                    Matrix(3, 3, \[ 0, 0, 1, 1, -1, 1, 1, 0, 0 ]),
                    Matrix(3, 3, \[ 0, -1, 1, 0, -1, 0, 1, -1, 0 ])
                        /* order = 48 = 2^4 * 3 */ > |
                \[ -1, 1, 0, 0, 0, 1, 0, -1, 1 ],

                \[ -1, 0, 0, -1, 1, -1, 0, 0, -1 ],

                \[ 0, 0, -1, -1, 1, -1, -1, 0, 0 ],

                \[ 1, 0, 0, 1, -1, 1, 0, 0, 1 ],

                \[ 0, 1, 0, 0, 1, -1, -1, 1, -1 ],

                \[ 1, -1, 0, 0, 0, -1, 0, 1, -1 ],

                \[ -1, 1, -1, -1, 1, 0, 0, 1, 0 ],

                \[ 0, 0, -1, 0, -1, 0, -1, 0, 0 ],

                \[ 0, -1, 0, 1, -1, 0, 1, -1, 1 ],

                \[ 0, -1, 0, 0, -1, 1, 1, -1, 1 ],

                \[ 1, -1, 0, 1, 0, 0, 0, 1, -1 ],

                \[ -1, 1, 0, -1, 0, 0, 0, -1, 1 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 0, 1, -1, 0, 0, -1, 1, -1, 0 ],

                \[ 0, 1, 0, -1, 1, 0, -1, 1, -1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ 0, 0, 1, 1, -1, 1, 1, 0, 0 ],

                \[ 0, -1, 1, -1, 0, 0, -1, 1, 0 ],

                \[ -1, 1, -1, 0, 1, -1, 0, 1, 0 ],

                \[ 0, -1, 1, 0, 0, 1, -1, 1, 0 ],

                \[ 1, -1, 1, 1, -1, 0, 0, -1, 0 ],

                \[ 1, -1, 1, 0, -1, 1, 0, -1, 0 ],

                \[ 0, 0, 1, 0, 1, 0, 1, 0, 0 ],

                \[ 0, 1, -1, 1, 0, 0, 1, -1, 0 ]
            ],
            facetdata := [ PowerStructure(Rec) |
                rec<cellrec | 
                    vertices := \[ 1, 3, 4 ],
                    mover := \[ 1, 1, 0, 0, 1, 0, 0, 0, 1 ],
                    type := 1,
                    orientationstd := -1>,
                rec<cellrec | 
                    vertices := \[ 1, 3, 5 ],
                    mover := \[ 1, 0, 0, 0, 0, 1, 0, -1, 1 ],
                    type := 1,
                    orientationstd := -1>,
                rec<cellrec | 
                    vertices := \[ 3, 4, 5 ],
                    mover := \[ 0, 0, 1, -1, 0, 1, -1, 1, 0 ],
                    type := 1,
                    orientationstd := -1>,
                rec<cellrec | 
                    vertices := \[ 1, 4, 5 ],
                    mover := \[ 1, 1, 0, 0, 1, 1, 0, 0, 1 ],
                    type := 1,
                    orientationstd := 1>
            ],
            barycenter := \[ 2, 1, 0, 1, 2, 1, 0, 1, 2 ],
            facets := [ PowerSequence(IntegerRing()) |
                \[ 1, 3, 4 ],
                \[ 1, 3, 5 ],
                \[ 3, 4, 5 ],
                \[ 1, 4, 5 ]
            ]>
    ],
    [ PowerStructure(Rec) |
        rec<cellrec | 
            vertices := \[ 1, 2, 3, 4, 5 ],
            stabilizer := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ -1, 0, 0, 0, -1, 1, 0, 0, 1 ]),
                    Matrix(3, 3, \[ 0, 0, 1, 0, -1, 1, -1, 0, 0 ]),
                    ScalarMatrix(3, -1)
                        /* order = 16 = 2^4 */ > |
                \[ 0, 0, -1, -1, 1, -1, -1, 0, 0 ],

                \[ 0, 0, -1, 1, -1, 0, 1, 0, 0 ],

                \[ 0, 0, -1, 0, -1, 0, -1, 0, 0 ],

                \[ 1, 0, 0, 1, -1, 1, 0, 0, 1 ],

                \[ 0, 0, 1, 1, -1, 1, 1, 0, 0 ],

                \[ 0, 0, 1, 0, -1, 1, -1, 0, 0 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, 0, -1, 1, 0, 0, 1 ],

                \[ 1, 0, 0, 1, -1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, -1, 1, -1, 0, 0, -1 ],

                \[ 1, 0, 0, 0, 1, -1, 0, 0, -1 ],

                \[ 0, 0, -1, 0, 1, -1, 1, 0, 0 ],

                \[ 0, 0, 1, -1, 1, 0, -1, 0, 0 ],

                \[ 0, 0, 1, 0, 1, 0, 1, 0, 0 ],

                \[ -1, 0, 0, -1, 1, 0, 0, 0, 1 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ]
            ],
            stabilizerplus := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ -1, 0, 0, 0, -1, 1, 0, 0, 1 ]),
                    Matrix(3, 3, \[ 0, 0, 1, 0, -1, 1, -1, 0, 0 ]),
                    ScalarMatrix(3, -1)
                        /* order = 16 = 2^4 */ > |
                \[ 0, 0, -1, -1, 1, -1, -1, 0, 0 ],

                \[ 0, 0, -1, 0, -1, 0, -1, 0, 0 ],

                \[ 1, 0, 0, 1, -1, 1, 0, 0, 1 ],

                \[ 0, 0, 1, 1, -1, 1, 1, 0, 0 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, -1, 1, -1, 0, 0, -1 ],

                \[ 0, 0, 1, 0, 1, 0, 1, 0, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ]
            ],
            facetdata := [ PowerStructure(Rec) |
                rec<cellrec | 
                    vertices := \[ 1, 2, 3, 4 ],
                    mover := \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],
                    type := 1,
                    orientationstd := 1>,
                rec<cellrec | 
                    vertices := \[ 1, 2, 3, 5 ],
                    mover := \[ 0, 0, 1, 1, 0, 0, 0, 1, 0 ],
                    type := 1,
                    orientationstd := -1>,
                rec<cellrec | 
                    vertices := \[ 2, 3, 4, 5 ],
                    mover := \[ 0, 0, 1, -1, 1, 1, 0, 1, 0 ],
                    type := 1,
                    orientationstd := -1>,
                rec<cellrec | 
                    vertices := \[ 1, 3, 4, 5 ],
                    mover := \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],
                    type := 2,
                    orientationstd := -1>,
                rec<cellrec | 
                    vertices := \[ 1, 2, 4, 5 ],
                    mover := \[ 1, 0, 0, 0, 1, 1, 0, 0, 1 ],
                    type := 1,
                    orientationstd := -1>
            ],
            barycenter := \[ 2, 1, 0, 1, 3, 1, 0, 1, 2 ],
            facets := [ PowerSequence(IntegerRing()) |
                \[ 1, 2, 3, 4 ],
                \[ 1, 2, 3, 5 ],
                \[ 2, 3, 4, 5 ],
                \[ 1, 3, 4, 5 ],
                \[ 1, 2, 4, 5 ]
            ]>
    ],
    [ PowerStructure(Rec) |
        rec<cellrec | 
            vertices := \[ 1, 2, 3, 4, 5, 6 ],
            stabilizer := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ 0, 1, -1, 0, 1, 0, -1, 1, 0 ]),
                    Matrix(3, 3, \[ 0, 0, 1, 1, -1, 1, 0, -1, 1 ]),
                    Matrix(3, 3, \[ 0, 1, -1, 1, 0, -1, 0, 0, -1 ])
                        /* order = 48 = 2^4 * 3 */ > |
                \[ 0, 1, -1, 0, 1, 0, -1, 1, 0 ],

                \[ 0, 0, 1, 1, -1, 1, 1, 0, 0 ],

                \[ -1, 0, 0, -1, 0, 1, -1, 1, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 1, -1 ],

                \[ 0, 0, 1, -1, 0, 1, -1, 1, 0 ],

                \[ 1, -1, 0, 1, 0, -1, 1, 0, 0 ],

                \[ 0, -1, 1, 0, -1, 0, 1, -1, 0 ],

                \[ 0, -1, 1, -1, 0, 1, 0, 0, 1 ],

                \[ 0, 0, -1, -1, 1, -1, 0, 1, -1 ],

                \[ -1, 1, 0, 0, 1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, -1, 1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 1, 0, -1, 0, 1, 0, 0, 1 ],

                \[ -1, 1, 0, 0, 1, 0, 0, 1, -1 ],

                \[ 1, -1, 0, 0, -1, 0, 0, -1, 1 ],

                \[ 1, -1, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, -1, 1, -1, 0, 0, -1 ],

                \[ 0, 0, -1, -1, 1, -1, -1, 0, 0 ],

                \[ 0, 0, 1, 0, 1, 0, -1, 1, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 0, 0, 1, 1, -1, 1, 0, -1, 1 ],

                \[ 1, 0, 0, 1, -1, 1, 0, 0, 1 ],

                \[ -1, 0, 0, -1, 1, -1, -1, 1, 0 ],

                \[ 1, 0, 0, 1, 0, -1, 1, -1, 0 ],

                \[ 0, 0, -1, 0, -1, 0, 1, -1, 0 ],

                \[ 1, -1, 0, 1, 0, -1, 0, 0, -1 ],

                \[ 1, 0, 0, 1, 0, -1, 0, 1, -1 ],

                \[ 0, -1, 1, 0, -1, 0, -1, 0, 0 ],

                \[ -1, 0, 0, -1, 0, 1, 0, -1, 1 ],

                \[ 0, 1, -1, 1, 0, -1, 1, 0, 0 ],

                \[ 0, 0, 1, -1, 0, 1, 0, -1, 1 ],

                \[ 0, 0, -1, 1, 0, -1, 0, 1, -1 ],

                \[ 1, -1, 0, 1, -1, 1, 1, 0, 0 ],

                \[ -1, 1, 0, -1, 1, -1, 0, 1, -1 ],

                \[ 0, 0, -1, 1, 0, -1, 1, -1, 0 ],

                \[ 0, 0, 1, 0, 1, 0, 1, 0, 0 ],

                \[ 0, -1, 1, 1, -1, 1, 1, -1, 0 ],

                \[ -1, 1, 0, -1, 0, 1, -1, 0, 0 ],

                \[ -1, 1, 0, -1, 1, -1, -1, 0, 0 ],

                \[ 0, 0, -1, 0, -1, 0, -1, 0, 0 ],

                \[ 0, -1, 1, -1, 0, 1, -1, 0, 0 ],

                \[ 0, 1, -1, -1, 1, -1, 0, 0, -1 ],

                \[ 1, -1, 0, 1, -1, 1, 0, -1, 1 ],

                \[ 0, -1, 1, 1, -1, 1, 0, 0, 1 ],

                \[ 0, 1, -1, 0, 1, 0, 1, 0, 0 ],

                \[ 1, 0, 0, 1, -1, 1, 1, -1, 0 ],

                \[ 0, 1, -1, -1, 1, -1, -1, 1, 0 ],

                \[ 0, 1, -1, 1, 0, -1, 0, 0, -1 ]
            ],
            stabilizerplus := [ MatrixGroup<3, IntegerRing() |
                    Matrix(3, 3, \[ 0, 1, -1, 0, 1, 0, -1, 1, 0 ]),
                    Matrix(3, 3, \[ 0, 0, 1, 1, -1, 1, 0, -1, 1 ]),
                    Matrix(3, 3, \[ 0, 1, -1, 1, 0, -1, 0, 0, -1 ])
                        /* order = 48 = 2^4 * 3 */ > |
                \[ 0, 1, -1, 0, 1, 0, -1, 1, 0 ],

                \[ 0, 0, 1, 1, -1, 1, 1, 0, 0 ],

                \[ -1, 0, 0, -1, 0, 1, -1, 1, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 1, -1 ],

                \[ 0, 0, 1, -1, 0, 1, -1, 1, 0 ],

                \[ 1, -1, 0, 1, 0, -1, 1, 0, 0 ],

                \[ 0, -1, 1, 0, -1, 0, 1, -1, 0 ],

                \[ 0, -1, 1, -1, 0, 1, 0, 0, 1 ],

                \[ 0, 0, -1, -1, 1, -1, 0, 1, -1 ],

                \[ -1, 1, 0, 0, 1, 0, 0, 0, 1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, -1, 1 ],

                \[ -1, 0, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 1, 0, -1, 0, 1, 0, 0, 1 ],

                \[ -1, 1, 0, 0, 1, 0, 0, 1, -1 ],

                \[ 1, -1, 0, 0, -1, 0, 0, -1, 1 ],

                \[ 1, -1, 0, 0, -1, 0, 0, 0, -1 ],

                \[ -1, 0, 0, -1, 1, -1, 0, 0, -1 ],

                \[ 0, 0, -1, -1, 1, -1, -1, 0, 0 ],

                \[ 0, 0, 1, 0, 1, 0, -1, 1, 0 ],

                \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],

                \[ 0, 0, 1, 1, -1, 1, 0, -1, 1 ],

                \[ 1, 0, 0, 1, -1, 1, 0, 0, 1 ],

                \[ -1, 0, 0, -1, 1, -1, -1, 1, 0 ],

                \[ 1, 0, 0, 1, 0, -1, 1, -1, 0 ],

                \[ 0, 0, -1, 0, -1, 0, 1, -1, 0 ],

                \[ 1, -1, 0, 1, 0, -1, 0, 0, -1 ],

                \[ 1, 0, 0, 1, 0, -1, 0, 1, -1 ],

                \[ 0, -1, 1, 0, -1, 0, -1, 0, 0 ],

                \[ -1, 0, 0, -1, 0, 1, 0, -1, 1 ],

                \[ 0, 1, -1, 1, 0, -1, 1, 0, 0 ],

                \[ 0, 0, 1, -1, 0, 1, 0, -1, 1 ],

                \[ 0, 0, -1, 1, 0, -1, 0, 1, -1 ],

                \[ 1, -1, 0, 1, -1, 1, 1, 0, 0 ],

                \[ -1, 1, 0, -1, 1, -1, 0, 1, -1 ],

                \[ 0, 0, -1, 1, 0, -1, 1, -1, 0 ],

                \[ 0, 0, 1, 0, 1, 0, 1, 0, 0 ],

                \[ 0, -1, 1, 1, -1, 1, 1, -1, 0 ],

                \[ -1, 1, 0, -1, 0, 1, -1, 0, 0 ],

                \[ -1, 1, 0, -1, 1, -1, -1, 0, 0 ],

                \[ 0, 0, -1, 0, -1, 0, -1, 0, 0 ],

                \[ 0, -1, 1, -1, 0, 1, -1, 0, 0 ],

                \[ 0, 1, -1, -1, 1, -1, 0, 0, -1 ],

                \[ 1, -1, 0, 1, -1, 1, 0, -1, 1 ],

                \[ 0, -1, 1, 1, -1, 1, 0, 0, 1 ],

                \[ 0, 1, -1, 0, 1, 0, 1, 0, 0 ],

                \[ 1, 0, 0, 1, -1, 1, 1, -1, 0 ],

                \[ 0, 1, -1, -1, 1, -1, -1, 1, 0 ],

                \[ 0, 1, -1, 1, 0, -1, 0, 0, -1 ]
            ],
            facetdata := [ PowerStructure(Rec) |
                rec<cellrec | 
                    vertices := \[ 1, 2, 3, 4, 5 ],
                    mover := \[ 1, 0, 0, 0, 1, 0, 0, 0, 1 ],
                    type := 1,
                    orientationstd := 1>,
                rec<cellrec | 
                    vertices := \[ 1, 2, 3, 4, 6 ],
                    mover := \[ 1, -1, 1, 0, -1, 1, 0, 0, 1 ],
                    type := 1,
                    orientationstd := -1>,
                rec<cellrec | 
                    vertices := \[ 2, 3, 4, 5, 6 ],
                    mover := \[ 0, 0, 1, -1, 0, 1, 0, -1, 1 ],
                    type := 1,
                    orientationstd := 1>,
                rec<cellrec | 
                    vertices := \[ 1, 2, 3, 5, 6 ],
                    mover := \[ 1, 0, 0, 0, 1, 0, 0, 1, -1 ],
                    type := 1,
                    orientationstd := 1>,
                rec<cellrec | 
                    vertices := \[ 1, 2, 4, 5, 6 ],
                    mover := \[ 0, 1, 0, 1, 0, 1, 0, 0, 1 ],
                    type := 1,
                    orientationstd := -1>,
                rec<cellrec | 
                    vertices := \[ 1, 3, 4, 5, 6 ],
                    mover := \[ 1, -1, 1, 0, -1, 1, 0, -1, 0 ],
                    type := 1,
                    orientationstd := -1>
            ],
            barycenter := \[ 3, 2, 1, 2, 4, 2, 1, 2, 3 ],
            facets := [ PowerSequence(IntegerRing()) |
                \[ 1, 2, 3, 4, 5 ],
                \[ 1, 2, 3, 4, 6 ],
                \[ 2, 3, 4, 5, 6 ],
                \[ 1, 2, 3, 5, 6 ],
                \[ 1, 2, 4, 5, 6 ],
                \[ 1, 3, 4, 5, 6 ]
            ]>
    ]
]
;