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A novel graphene antenna composed of a graphene dipole and four auxiliary graphene sheets oriented at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>90</mn><mo>∘</mo></msup></semantics></math></inline-formula> to each other is proposed and analyzed. The sheets play the role of reflectors. A detailed group-theoretical analysis of symmetry properties of the discussed antennas has been completed. Through electric field control of the chemical potentials of the graphene elements, the antenna can provide a quasi-omnidirectional diagram, a one- or two-directional beam regime, dynamic control of the beam width and, due to the vertical orientation of the dipole with respect to the base substrate, a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>360</mn><mo>∘</mo></msup></semantics></math></inline-formula> beam steering in the azimuth plane. An additional graphene layer on the base permits control of the radiation pattern in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>-direction. Radiation patterns in different working states of the antenna are considered using symmetry arguments. We discuss the antenna parameters such as input reflection coefficient, total efficiency, front-to-back ratio, and gain. An equivalent circuit of the antenna is suggested. The proposed antenna operates at frequencies between 1.75 THz and 2.03 THz. Depending on the active regime defined by the chemical potentials set on the antenna graphene elements, the maximum gain varies from 0.86 to 1.63.