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Let's see whether there are any stars or other notable night sky features in Gemini, which remain to be inserted in my star list:

First the Greek lettered stars. Currently I have the following 11 in my list, beginning with Tejat Prior and ending with Pollux:

Tejat Prior η Gemini 3.31 22° 31′ N 06h 12m 94.4
Tejat Posterior μ Gemini 2.87 22° 32′ N 06h 20m 96.4
Mebsuta ε Gemini 3.06 25° 11′ N 06h 41m 101.7
Alhena γ Gemini 1.93 16° 27′ N 06h 53m 104.8
  ω Gemini 5.20 24° 13′ N 06h 59m 106.4

Alzirr

 ξ Gemini 3.35 12° 54′ N 07h 01m 106.7

Wasat

 δ Gemini 3.50 22° 05′ N 07h 17m 110.8

 

 ρ Gemini 4.16 31° 47′ N 07h 26m 113.1

Castor (419)

 α Gemini 1.58 32° 00′ N 07h 31m 114.4

 

 σ Gemini 4.23 28° 53′ N 07h 40m 116.7

Pollux

 β Gemini 1.16 28° 09′ N 07h 42m 117.2

To these should be added ν, θ, ζ, τ, λ, ι, υ, ο, κ, π, φ, and χ, i.e. 12 more:

Tejat Prior 06h14m52.70s 06h14.878m

94.4
ν 06h28m57.79s 06h28.963m

98.0
θ 06h52m47.34s 06h52.789m

104.0
ζ 07h04m06.54s 07h04.109m

106.9
τ 07h11m08.39s 07h11.140m

108.7
λ 07h18m05.61s 07h18.094m

110.4
ι 07h25m43.68s 07h25.728m

112.4
υ 07h35m55.37s 07h35.923m

115.0
ο 07h39m09.96s 07h39.166m

115.8
κ 07h44m26.87s 07h44.448m

117.1
π 07h47m30.34s 07h47.506m

117.9
φ 07h53m29.84s 07h53.497m

119.4
χ 08h03m31.10s 08h03.518m

122.0
  ν Gemini 4.13 20° 13′ N  06h 26m 98.0
  θ Gemini 3.60 33° 58′ N 06h 50m 104.0
Mekbuda ζ Gemini 4.01 20° 34′ N 07h 01m 106.9
  τ Gemini 4.41 30° 15′ N 07h 09m 108.7
  λ Gemini 3.58 16° 32′ N 07h 15m 110.4
Propus ι Gemini 3.78 27° 48′ N 07h 23m 112.4
  υ Gemini 4.06 26° 54′ N 07h 33m 115.0
  ο Gemini 4.89 34° 35′ N 07h 37m 115.8
  κ Gemini 3.57 24° 24′ N 07h 42m 117.1
  π Gemini 5.14 33° 25′ N 07h 45m 117.9
  φ Gemini 4.97 26° 46′ N 07h 51m 119.4
  χ Gemini 4.94 27° 48′ N  08h 01m 122.0

"Mekbuda is from Al Makbūda, Contracted, the Arabic designation for the drawn-in paw of the ancient Asad; but some, with less probability, derive it from Al Mutakabbidah, a Culminating Star." (Allen)

"ι is Propus in the Standard Dictionary, although it lies between the shoulders of the Twins ... Propus [η] is from the Πρόπους of Hipparchos and Ptolemy, indicating its position in front of Castor's left foot, and is its universal title, with the equivalent Praepes ..." (Allen)