A sphere.
All other solids, including cubes, rectangular prisms, and cones all have at least one vertex.
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triangular prism
Because the base of a cone is round, it is the only three dimensional figure with only one vertex.
A dodecagon has 12 sides. Whether or not from one vertex, the number of sides remains the same. Each vertex is formed when 2 sides meet.
To have a parabola with only one x-intercept, the vertex of the parabola must lie on the x-axis. This means the parabola opens either upwards or downwards, depending on the coefficient of the squared term in the equation. If the coefficient is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. By adjusting the coefficients in the equation of the parabola, you can position the vertex such that there is only one x-intercept.
There can be 14 lines in a seven side shape * * * * * That is the total number of diagonals from ALL vertices. Not what the question asked, though. From one vertex, there can be 4. One to every other vertex except for itself and one each on either side.