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      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F23_E",
        "F23_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F23_F",
        "F23_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F23_A",
        "F23_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F23_B",
        "F23_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F23_C",
        "F23_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_A",
        "F24_B"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_B",
        "F24_C"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_C",
        "F24_A"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_D",
        "F24_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_E",
        "F24_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_F",
        "F24_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_A",
        "F24_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_B",
        "F24_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F24_C",
        "F24_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_A",
        "F25_B"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_B",
        "F25_C"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_C",
        "F25_A"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_D",
        "F25_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_E",
        "F25_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_F",
        "F25_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_A",
        "F25_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_B",
        "F25_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F25_C",
        "F25_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_A",
        "F26_B"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_B",
        "F26_C"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_C",
        "F26_A"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_D",
        "F26_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_E",
        "F26_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_F",
        "F26_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_A",
        "F26_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_B",
        "F26_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F26_C",
        "F26_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_A",
        "F27_B"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_B",
        "F27_C"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_C",
        "F27_A"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_D",
        "F27_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_E",
        "F27_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_F",
        "F27_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_A",
        "F27_D"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_B",
        "F27_E"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "points": [
        "F27_C",
        "F27_F"
      ],
      "color": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    }
  ],
  "aux_lines": [
    {
      "points": [
        "P0",
        "P"
      ],
      "color": "#d97400",
      "dash": true,
      "depthTest": false,
      "width": 4.0
    },
    {
      "points": [
        "F0_base",
        "F0_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    },
    {
      "points": [
        "F1_base",
        "F1_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    },
    {
      "points": [
        "F2_base",
        "F2_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    },
    {
      "points": [
        "F3_base",
        "F3_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    },
    {
      "points": [
        "F4_base",
        "F4_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    }
  ],
  "aux_faces": [],
  "aux_points": [
    "P",
    "F0_top",
    "F1_top",
    "F2_top"
  ],
  "labels": [
    {
      "text": "P",
      "point": "P",
      "offset": [
        0.08,
        0.12,
        0.08
      ],
      "kind": "aux"
    },
    {
      "text": "F1",
      "point": "F0_top",
      "offset": [
        0.07,
        0.12,
        0.07
      ],
      "kind": "aux"
    },
    {
      "text": "F2",
      "point": "F1_top",
      "offset": [
        0.07,
        0.12,
        0.07
      ],
      "kind": "aux"
    },
    {
      "text": "F3",
      "point": "F2_top",
      "offset": [
        0.07,
        0.12,
        0.07
      ],
      "kind": "aux"
    }
  ],
  "primitives": [],
  "height_map": [
    [
      1,
      0,
      2,
      1,
      0
    ],
    [
      0,
      3,
      1,
      0,
      2
    ],
    [
      2,
      1,
      4,
      0,
      1
    ],
    [
      0,
      2,
      0,
      1,
      2
    ]
  ],
  "floating_units": [
    {
      "x": 1,
      "z": 0,
      "layer": 3
    },
    {
      "x": 4,
      "z": 0,
      "layer": 2
    },
    {
      "x": 3,
      "z": 2,
      "layer": 4
    },
    {
      "x": 0,
      "z": 3,
      "layer": 3
    },
    {
      "x": 3,
      "z": 3,
      "layer": 5
    }
  ],
  "base_unit": "triangular_prism",
  "qa_seeds": [
    {
      "task": "GE3D_BASE_STACK_TOTAL_COUNT",
      "question": "How many triangular prisms are in the stack?",
      "answer": 28,
      "evidence": "Sum all nonzero column heights and any explicitly floating solids."
    },
    {
      "task": "GE3D_BASE_STACK_MAX_HEIGHT",
      "question": "What is the maximum number of base solids in one vertical position?",
      "answer": 4,
      "evidence": "Count stacked and floating solids at each vertical grid position."
    },
    {
      "task": "GE3D_BASE_STACK_TOP_COLUMN_COUNT",
      "question": "How many vertical positions reach the highest occupied layer?",
      "answer": 1,
      "evidence": "Count positions whose highest occupied layer equals the scene maximum."
    },
    {
      "task": "GE3D_BASE_STACK_HIGHEST_LAYER",
      "question": "What is the highest occupied layer number if the ground layer is layer 1?",
      "answer": 6,
      "evidence": "Find the largest occupied layer index and convert it to one-based numbering."
    },
    {
      "task": "GE3D_BASE_STACK_OCCUPIED_POSITIONS",
      "question": "How many ground positions are occupied by at least one base solid?",
      "answer": 13,
      "evidence": "Count nonzero cells in the ground height map."
    },
    {
      "task": "GE3D_BASE_STACK_MARKED_COLUMN_HEIGHT",
      "question": "How many base solids are in the marked vertical position P?",
      "answer": 4,
      "evidence": "The orange dashed line and P label mark the selected column."
    },
    {
      "task": "GE3D_BASE_STACK_TALL_COLUMN_COUNT",
      "question": "How many occupied vertical positions contain at least two base solids?",
      "answer": 8,
      "evidence": "Count vertical positions with two or more occupied layers."
    },
    {
      "task": "GE3D_BASE_STACK_EMPTY_POSITIONS",
      "question": "How many ground positions are empty?",
      "answer": 7,
      "evidence": "Count cells in the sparse height map with height zero."
    },
    {
      "task": "GE3D_BASE_STACK_ABOVE_GROUND_COUNT",
      "question": "How many base solids are above the first layer?",
      "answer": 15,
      "evidence": "For each column, count all layers above the ground layer."
    },
    {
      "task": "GE3D_BASE_STACK_THIRD_LEVEL_COLUMN_COUNT",
      "question": "How many vertical positions have a solid on the third layer or higher?",
      "answer": 7,
      "evidence": "Count positions whose highest occupied layer is at least the third layer."
    },
    {
      "task": "GE3D_BASE_STACK_FLOATING_COUNT",
      "question": "How many base solids are floating above a gap or empty cell?",
      "answer": 5,
      "evidence": "Count solids listed in the nonphysical floating layer set."
    },
    {
      "task": "GE3D_BASE_STACK_FLOATING_POSITION_COUNT",
      "question": "How many grid positions contain at least one floating solid?",
      "answer": 5,
      "evidence": "Count distinct grid positions used by floating solids."
    },
    {
      "task": "GE3D_BASE_STACK_HIGHEST_FLOATING_LAYER",
      "question": "What is the highest layer number occupied by a floating solid?",
      "answer": 6,
      "evidence": "Find the maximum floating layer index and convert it to one-based numbering."
    }
  ],
  "_augmentation": "base_stack_v4",
  "_hide_meta_panel": true,
  "_id": "base_stack_v4_tri_prism",
  "_model": "rule_base_stack_v4"
}