"Minivelo" bicycles are bicycles with small, 20" wheels but with road or city / hybrid bike design influences rather than the BMX bike look. Though at a glance these compact bicycles look like they might be folders, they're not typically folding bicycles.
Because the small size lends to easier storage, minivelo bikes are hugely popular in some Asian countries, Japan, Korea and Taiwan in particular. They have a following in Europe and the UK, also. These lightweight bicycles "feel" a lot like a normal bike. Unlike many comparably equipped folding bikes, they tend to be reasonably stiff and responsive. Many people carry minivelo bicycles onto light rail and train systems as part of a multimodal commute.
Organic Wheels in Oregon Spinburn minivelo bicycles for the US market under the "Minivelo USA" brand. Purchase is currently online through PayPal, with bikes ranging in price from about $700 for 7005 aluminum bike equipped with brand X components up to almost $1500 for the SRAM Rival equipped "Minivelo USA Race" on a Reynolds 525 CroMoly double butted steel frame and carbon front fork.
The "Reach" line of folding bikes from Rad Innovations is clearly inspired by Asian minivelo bikes. They're meant more for traveling rather than multimodal commutes -- they pack into a size that will fit a standard suitcase, so the folding is not as compact or quick as many folders. The ride, however, is surprisingly nimble. There's not the squirrelly feel that's typical of many compact folding bikes, probably because of the somewhat longer wheelbase. Rad Innovations has suspension front and rear to make up for the inherent bumpiness of smaller wheels. The suspension adds just enough give to take up road shock without adding a lot of weight. The Reach bicycles I've tried felt a lot like a "normal" bicycle -- the Rad Innovations people did a very good job of designing this bike.
Rad Innovations Reach range from $1000 for a Shimano Alivio eqiupped bicycle up to $1500 for a Tiagra equipped bike. All Reach bikes are 7005 aluminum. Reach bikes are available through local dealers.
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I've only tried the Reach bike with that funky parallelogram front suspension. I was surprised at how "normal" the ride is -- none of the weird handling that you usually get with small wheel folding bikes. I've never tried a true minivelo bike, though.
They look like they're a bit shorter, but that little bit could make a huge difference in some situations. I also imagine they'd be a lot easier to carry.
That is described on Google as a velomobile. I was looking at velomobiles in Flickr then searched for more. Very funny- I must have had the most dumfounded look on my face!