Question: The Rigi, is a mountain massif of the Alps, located in Central Switzerland, the range is in the Schwyzer Alps, and is split between the cantons of Lucerne, and which canton in central Switzerland between the Alps in the south, Lake Lucerne to the west, and which lake in the north?

Context articles: Lucerne
List of mountains of the canton of Schwyz
Rigi Railways
Dosse (Rigi)
Uri Alps
Canton of Schwyz
North-Eastern Swiss Alps
Rigi
Rigi Kaltbad
Rigi Hochflue

Lucerne ( ; German: "Luzern" ] ; French: "Lucerne" ] ; Italian: "Lucerna" ] ; Romansh: "Lucerna" ; Lucerne Swiss-German: "Lozärn") is a city in central Switzerland, in the German-speaking portion of the country.
 Lucerne is the capital of the canton of Lucerne and part of the district of the same name.
 With a population of about 81,057 people (as of 2013 ), Lucerne is the most populous town in Central Switzerland, and a nexus of economics, transportation, culture, and media of this region.
 The city's urban area consists of 17 municipalities and towns located in three different cantons with an overall population of about 250,000 people (as of 2007 ).
This is a list of mountains of the Swiss canton of Schwyz.
 Schwyz is a very mountainous canton and lies almost entirely within the Alps.
 It is also one of the 15 cantons having summits above 2,000 metres.
 Topographically, the two most important summits of the canton are those of the Bös Fulen (most elevated) and the Rigi (most prominent and isolated).
 All of the mountains of the canton are part of the Schwyzer Alps mountain range, although not all the mountains of that range lie within the canton.
Rigi Railways (German: "Rigi Bahnen" ) is a group of railways on the mountain Rigi, located between two of the arms of Lake Lucerne, in Switzerland.
 They include two standard gauge rack railways, the Vitznau–Rigi Bahn (VRB) and the Arth–Rigi Bahn (ARB), along with the Luftseilbahn Weggis–Rigi Kaltbad (LWRK) cable car and six smaller cable cars: Luftseilbahn Kräbel–Rigi Scheidegg (LKR), Luftseilbahn Obergschwend–Rigi Burggeist (LORB), Luftseilbahn Küssnacht–Seebodenalp (LKüS), Luftseilbahn Vitznau–Hinterbergen (LVH), Luftseilbahn Vitznau–Wissifluh (LVW), and Luftseilbahn Brunnen–Urmiberg (LBU).
The Dosse (Germanized: "Dossen", 1684 m ) is a mountain of the Rigi massif, located on the border between the Swiss cantons of Lucerne and Schwyz.
 The mountain overlooks Lake Lucerne, near Vitznau.
 It is the highest point of the massif in the canton of Lucerne.
 The lightly lower peak only 200m northwest of it is called Chli Dosse (1669 m ).
The Uri Alps (German: "Urner Alps" ) are a mountain range in Central Switzerland and part of the Western Alps.
 They extend into the cantons of Obwalden, Valais, Bern, Uri and Nidwalden and are bordered by the Bernese Alps (Grimsel Pass) and the Emmental Alps to the west (the four lakes: Lungerersee, Sarnersee, Wichelsee, and Alpnachersee), the Schwyzer Alps to the north (Lake Lucerne), the Lepontine Alps to the south (the valley of Urseren with Andermatt) and the Glarus Alps to the east (Reuss).
The canton of Schwyz (] ) is a canton in central Switzerland between the Alps in the south, Lake Lucerne to the west and Lake Zürich in the north, centered on and named after the town of Schwyz.
This article focuses on the part of the Alps and Pré-Alps that is located in North-Eastern Switzerland and compromises the Schwyzer Alps and the Appenzell Alps.
 This region is bordered by: Lake Lucerne in the south-west; the Klausen Pass, upper Linth valley and Lake Walen in the south; the Rhine valley in the east; Lake Constance in the north.
The Rigi (or "Mount Rigi"; also known as "Queen of the Mountains") is a mountain massif of the Alps, located in Central Switzerland.
 The whole massif is almost entirely surrounded by the water of three different water bodies: Lake Lucerne, Lake Zug and Lake Lauerz.
 The range is in the Schwyzer Alps, and is split between the cantons of Schwyz and Lucerne, although the main summit, named "Rigi Kulm", at 1,798 meters above sea level, lies within the canton of Schwyz.
Rigi Kaltbad is a resort in the Swiss Alps, located in the canton of Lucerne.
 The resort sits on a sunny terrace at a height of 1,433 metres, overlooking Lake Lucerne above Weggis in Central Switzerland.
 The locality is part of the municipality of Weggis.
The Rigi Hochflue is a mountain summit west of the mountain range Urmiberg, in itself part of the Rigi massif, overlooking the "Gersauerbecken" of Lake Lucerne in Central Switzerland on its mountainside to the south, and Lake Lauerz on its north side.
 It has an elevation of 1698 m above sea level and is located in the canton of Schwyz.