There is such a ticket.
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The Tageskarte EURegio Bodensee is a ticket allowing a day's unlimited travel in the areas surrounding the lake, irrespective of country.
Several versions of the Tageskarte are available. The area of validity is split into three zones, with tickets available for one zone, two adjoining zones or all three.
Tageskarte Zone 1 (east) covers the eastern part of the lake and surrounding areas.
In Austria, validity extends over part of the Vorarlberg region, covering the towns of Bregenz, Dornbirn and Feldkirch.
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The Tageskarte can also be used on the local bus networks in the area.
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...and local "Stadtbus" (town bus) networks such as here in Feldkirch.
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Within Germany, most of the area bordering Lake Constance is in Baden-Württemberg state. At the eastern end of the lake, however, the town of Lindau lies within Bavaria.
ÖBB trains cross the border to terminate at Lindau.
The Tageskarte EURegio Bodensee can be used in and around Lindau...
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... on the regional bus services heading out of town...
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Some trains are operated by DBRegio (right), others by ALEX (below).
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Within Germany, Tageskarte is not valid on inter-city trains
On the opposite shore of the lake, Zone 1 extends into Switzerland.
A variety of transport operators provide the transport network in this area.
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PostAuto use double-deck buses on some routes. In this scenic area, the views from the upper deck are particularly good.
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A Tageskarte valid for Zone 1 can be used on bus services in this area irrespective of operator.
A couple of services operated by RegioBus enter Tageskarte's area of validity, in and around St Gallen.
The Tageskarte can also be used on Rheintal Bus (RTB) services, where these operate within the area.
Although illustrating Rheintal Bus, this image was taken in Buchs, outside the Tageskarte's area of validity.
The town of Rorschach, on the shore of the lake, has a small network of local bus routes. These operate under the "Seebus" name.
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Others are provided by private companies.
All accept Tageskarte within the relevant Zone.
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This one climbs out of the city of St Gallen, also using the rack-and-pinion system on steep gradients.
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A Tageskarte valid in Zone 1 can be used on St Gallen's bus network
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St Gallen's bus system is one of two within the Tageskarte's area where trolleybuses operate.
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I may be stretching it a little to claim that trams are one of the modes on which the Tageskarte EURegio Bodensee can be used. None of the towns or cities in the area of coverage have tram systems as such.
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Trains on the "Trogenerbahn", operated by Appenzeller Bahnen, run on-street into the centre of St Gallen.
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Both towns lie in an overlap between Zone 1 (east) and Zone 2 (central). A Tageskarte valid in either zone can be used on the ferry.
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Another ferry links Meersburg, on the northern shore of the lake, with the city of Konstanz.
A Tageskarte valid for Zone 2 is valid on the ferry.
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As well as foot passengers, bus passengers can also use a Zone 2 Tageskarte on routes which use the ferry.
Two interurban routes use the ferry to reach Konstanz from towns on and around the north shore of the lake.
There is a sizeable overlap between Zone 2 (central) and Zone 3 (west), covering parts of both Germany and Switzerland.
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Not all do, however.
The rail network also provides a number of interurban and regional links in this part of Germany. Local train services are provided by several companies.
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Double-deck trains operate a limited-stop inter-regional service from Konstanz to Karlsruhe. A Zone 2 Tageskarte is valid on this service as far Radolfzell, while a Zone 3 ticket can be used as far as Engen.
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Local trains between Konstanz, Radolzell and Engen are operated as "Seehas".
Although the route is entirely within Germany, the trains are operated by a subsidiary of SBB, the Swiss national operator.
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Hohenzollerische Landesbahn (HzL) operates the line from Radolfzell to Stockach.
Zone 3 only covers part of the route, but a Tageskarte valid for Zone 2 can be used throughout.
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These images were taken in Konstanz, which lies right on the border with Switzerland.
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Both Konstanz and Kreuzlingen lie within the area where Zones 2 and 3 overlap.
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As in Zone 1, interurban and rural bus services in Zones 2 and 3 are generally provided by PostAuto, although there are some exceptions.
This image was taken at Kreuzlingen railway station where buses connect with local rail services.
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Route 925 provides the bus link between Kreuzlingen and Konstanz at these times.
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"Thurbo" is the brand name used for a network of local train services in and around the Swiss canton of Thurgau. Most of Thurgau lies within the area covered by the Tageskarte (Zones 2 and/or 3), although the southern part of the canton is beyond the Tageskarte boundary.
Beyond the overlapping area of Zones 2 and 3, Zone 3 extends further west in both Germany and Switzerland, reaching the Swiss city of Schaffhausen.
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The trolleybus route forms part of a network of local bus routes within Schaffhausen.
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In the centre of Schaffhausen, the railway station forms an interchange hub between trains, city bus and trolleybus routes, and buses into the surrounding area.
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Others are provided by PostAuto.
Rheinfall ("Rhine Falls" in English) is one of Europe's largest waterfalls, on the river Rhine close to Schaffhausen. A railway line leaves Schaffhausen, then crosses the Rhine just above Rheinfall. A Tageskarte valid in Zone 3 can be used on this section of line.
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So there it is. Tageskarte EURegio Bodensee can be used on buses, trolleybuses, tram-trains, trains, ferries and a funicular. Six modes, in parts of Austria, Germany and Switzerland. It is priced in both Euro and the Swiss Franc.
At the time of writing, a ticket valid in one zone is priced at €18, or 26CHF. A two-zone ticket costs €24 / 35CHF; a ticket valid across all three zones costs €31 / 45CHF. Group tickets, for up to 2 adults and up to 4 children travelling together, are also available for the same or less than the cost of two individual adult tickets.
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The Tageskarte EURegio Bodensee is not the only example of a day ticket valid in three countries. I have previously written about the euregioticket valid in the Dutch, German and Belgian border regions.