## Step 1: Define the symbolic representation of the variables
The variables are 'reconnaissance troops', 'logistics companies', and 'medical platoons', which we will denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_0$ : reconnaissance troops
- $x_1$ : logistics companies
- $x_2$ : medical platoons

## 3: Define the objective function using symbolic variables
The objective function to maximize is: $6x_0^2 + 5x_0x_1 + 9x_1^2 + 3x_1x_2 + 6x_2^2 + x_0$

## 4: List the constraints using symbolic variables
The constraints are:
- $2.32x_0 + 4.68x_1 + 1.72x_2 \leq 47$ (logistical capacity constraint, but we have specific constraints for combinations of variables)
- $2.32x_0 \leq r_0$ 
- $4.51x_0 \leq r_1$
- $4.68x_1 \leq r_0$
- $4.38x_1 \leq r_1$
- $1.72x_2 \leq r_0$
- $2.0x_2 \leq r_1$
- $2.32x_0 + 1.72x_2 \leq 26$ 
- $2.32x_0 + 4.68x_1 \leq 17$
- $2.32x_0 + 4.68x_1 + 1.72x_2 \leq 17$
- $4.38x_1^2 + 2.0x_2^2 \leq 35$ (deployment weight constraint for $x_1$ and $x_2$)
- $4.51x_0 + 2.0x_2 \leq 29$ 
- $4.51x_0 + 4.38x_1 + 2.0x_2 \leq 29$

However, upon closer inspection, we see that $r_0$ and $r_1$ have upper bounds but are not directly used as constraints in a traditional sense. Instead, we focus on the given constraints:
- $2.32x_0 + 1.72x_2 \leq 26$
- $2.32x_0 + 4.68x_1 \leq 17$
- $2.32x_0 + 4.68x_1 + 1.72x_2 \leq 17$
- $4.38x_1^2 + 2.0x_2^2 \leq 35$
- $4.51x_0 + 2.0x_2 \leq 29$
- $4.51x_0 + 4.38x_1 + 2.0x_2 \leq 29$

## 5: Define the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'reconnaissance troops'), ('x1', 'logistics companies'), ('x2', 'medical platoons')],
    'objective_function': '6*x0^2 + 5*x0*x1 + 9*x1^2 + 3*x1*x2 + 6*x2^2 + x0',
    'constraints': [
        '2.32*x0 + 1.72*x2 <= 26',
        '2.32*x0 + 4.68*x1 <= 17',
        '2.32*x0 + 4.68*x1 + 1.72*x2 <= 17',
        '4.38*x1^2 + 2.0*x2^2 <= 35',
        '4.51*x0 + 2.0*x2 <= 29',
        '4.51*x0 + 4.38*x1 + 2.0*x2 <= 29',
        'x0 >= 0 and x0 == int(x0)',
        'x1 >= 0 and x1 == int(x1)',
        'x2 >= 0 and x2 == int(x2)'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="reconnaissance_troops", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="logistics_companies", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="medical_platoons", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(6*x0**2 + 5*x0*x1 + 9*x1**2 + 3*x1*x2 + 6*x2**2 + x0, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2.32*x0 + 1.72*x2 <= 26)
    model.addConstr(2.32*x0 + 4.68*x1 <= 17)
    model.addConstr(2.32*x0 + 4.68*x1 + 1.72*x2 <= 17)
    model.addConstr(4.38*x1**2 + 2.0*x2**2 <= 35)
    model.addConstr(4.51*x0 + 2.0*x2 <= 29)
    model.addConstr(4.51*x0 + 4.38*x1 + 2.0*x2 <= 29)

    # Solve the model
    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Reconnaissance troops: {x0.varValue}")
        print(f"Logistics companies: {x1.varValue}")
        print(f"Medical platoons: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```