All the Chanukah menorot that I have seen each have separate oil cups / holders. Would it be permissible to have a "trough" with separate cups coming out of it and each one having a separate wick, so that all wicks share the same oil source?
The Kitzur Shulchan Aruch brings a case when one has a bowl filled with oil and places wicks around the perimeter to make a menorah. (Kitzur Shulchan Aruch 139:9)
הַנֵּרוֹת, יִהְיוּ בְּשׁוּרָה אַחַת בְּשָׁוֶה, לֹא אֶחָד גָּבוֹהַּ וְאֶחָד נָמוּךְ. וְיִהְיֶה הֶפְסֵק בֵּין נֵר לְנֵר, שֶׁלֹּא יִתְקָרֵב הַלַהַב שֶׁל זֶה לָזֶה וְיִהְיֶה כְּמוֹ מְדוּרָה. וּבְנֵרוֹת שֶׁל שַעֲוָה, יִהְיֶה הֶפְסֵק, שֶׁלֹּא יִתְחַמֵּם זֶה מִזֶּה וְתִטֹּף הַשַּׁעֲוָה וְיִתְקַלְקָלו. מִלֵּא קְעָרָה שֶׁמֶן וְהִקִּיפָּהּ פְּתִילוֹת, אִם כָּפָה עָלֶיהָ כְּלִי, כָּל פְּתִילָה עוֹלָה בִּשְׁבִיל נֵר אֶחָד. לֹא כָּפָה עָלֶיהָ כְּלִי, אֲפִלוּ לְנֵר אֶחָד, אֵינָהּ עוֹלָה, לְפִי שֶׁהִיא כִּמְדוּרָה. נֵר שֶׁיֶשׁ לוֹ שְׁנֵי פִּיוֹת אוֹ יוֹתֵר, לֹא יַדְלִיקוּ בוֹ שְנַיִם אֲפִלוּ בַּלַיְלָה הָרִאשׁוֹן, מִשּׁוּם דְּלֵיכָּא הֶכֵּר כַּמָּה נֵרוֹת מַדְלִיקִין
If one filled a dish with oil and placed wicks around its perimeter, and then if he covers it with a vessel that has separate openings for for each wick, each wick can be counted as one light; but if he did not cover it with a vessel, then it is not even counted as one light, because it is similar to a torch.
So it appears that the wicks may have one oil source as long as they have separate openings in which each wick can poke up through.
(Translation from the ArtScroll Kitzur, Vol. 4)
Yes you can learn this from Shulchan Aruch Orach Chayim 671, 3:
נר שיש לו שתי פיות, עולה לו בשביל שנים.
an oil lamp which has two "mouthpieces" is considered as two lamps.
Despite that this is not the topic of the Shulchan Aruch there, because the original text (Gemara Shabbat 23a) addresses two lamps for two persons, it is obvious that you can use it as two lamps for one man who wants to light two candles for the second day of Chanuka. It is in this way that the Tur used the statement of the Gemara for two candles of one man (Bet Yosef). We told about a specially manufactured lamp.
For a bowl in which there are several wicks, the Tur and SA Saif 4 required that the two wicks do emerge from a perforated lid in which the distance between two holes is at least the size of one finger width. (Bet Yosef seems thinks that if the distance between the two wicks is great enough to show that they are separated, we don't need any lid, but in SA he followed the Tur's opinion).
Poskim (in name of Terumat Hadashen) described special oil lamps called "lampe" used for Chanuka in which the separation between two wicks is clearly discerned. This kind of lamp is good enough.
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