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My 4 year old granddaughter, playing with molecular models, began making a cyclopentane ring, each of whose carbons bore a spiro-connected cyclopentane ring of its own , in the manner of spiro[4.4]nonane. If she hadn't run out of carbon atoms first, the result would have been a pentagonal crown, with the five outer cyclopentane rings perpendicular to the central one.

pentaspiro[4.0.46.0.411.0.416.0.421.05]pentacosane

I wonder if such an alkane has been synthesized. Its molecular formula would be $\ce{C25H40}$. I can't think of why the molecule would be unstable or sterically impossible, but I couldn't find it in a Google search on $\ce{C25H40}$.

In particular, I wonder if the five outer rings would be exactly perpendicular to the center one (eclipsed), or somewhat staggered.

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    $\begingroup$ Looks somewhat strained, but possible. The outer rings themselves won't be exactly planar, let alone perpendicular. $\endgroup$ – Ivan Neretin Nov 3 '16 at 10:55
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These polyspiro compounds such as the one you gave are known as [m,n]rotanes, where m is the size of the central ring and n is the size of the decorating rings. So, your compound would be called [5,5]-rotane.

A Reaxys search unfortunately doesn't show anything for [5,5]-rotane, but in general, many such compounds have been made. A lot of the articles are in German or French (there are quite a few such articles). However, I did find one in English: J. Am. Chem. Soc. 1998, 120 (2), 317–328.

The authors synthesised and obtained X-ray structures of a number of rotanes, among them [5,4]rotane, which is the closest to the [5,5] that you are looking for. I quote:

enter image description here

In [5.4]rotane (7), the cyclopentane ring adopts a slightly distorted envelope conformation: C(1), C(5), C(9), and C(17) form an almost perfect plane (mean deviation 0.021 Å), while the flap atom C(13) is located 0.684 Å above this plane. The cyclobutane rings at C(13) and C(9) are nearly planar (φ = 9.7°) and planar (φ = 0.2°), respectively. The remaining three cyclobutane rings are moderately puckered (φ = 23.1, 26.5, and 28.2°).

The torsion angle φ of cyclobutane refers to the angle between the two planes that define the molecule. A completely planar four-membered ring would have φ = 0°, and an increasing value of φ indicates greater deviation from planarity:

enter image description here

As you can see in the X-ray structure, the five attached cyclobutane rings do eclipse each other to a certain extent: the obvious exception is the ring fused to C(13). This is not a very surprising conclusion at all. The envelope conformation of unsubstituted cyclopentane is known to suffer from torsional strain (i.e. unfavourable eclipsing interactions between substituents). Carey and Sundberg's Advanced Organic Chemistry, Part A writes (pp 162–3):

There is minimal angle strain in cyclopentane, but considerable torsional strain is present. Cyclopentane is nonplanar and the two minimum energy geometries are the envelope and the half-chair. [...] The planar portions of both conformations have torsional strain owing to C−H and C−C bond eclipsing.

There's a ton more information in the paper, and I'd recommend giving it a read if you are interested - I just tried to pick out the parts directly relevant to your question here, since you indicated that you were interested in the conformation of such a compound.

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Fascinating molecule. I am not offering anything substantially, new or original here; merely here to confirm what has already been said. I couldn't find any evidence that suggests this particular molecule has been synthesised.

In particular, I wonder if the five outer rings would be exactly perpendicular to the center one (eclipsed), or somewhat staggered.

Now to specifically address this part of the question, (and also to complement @orthocresol's great answer), I drew out your molecule in Avogadro and performed a molecular mechanics geometry optimisation using the MMFF94s force field.

The visualisations of the results are given below ( I tried to take some screenshots from different perspectives)

(note: @Martin pointed out some funny business going on with the hydrogens in the old pictures, and I took a good, hard look at the file once again and saw the odd bridging hydrogen too. Anyway, I redid the calculation, and here's some new visualisations). I still stand by the conclsuions I drew earlier, though.

enter image description here enter image description here

Anyway, the ring strain in general doesn't seem to terrible. The "ornamental" rings are not planar, and do look staggered to me. I also reckon this is chiral ($C_1$) symmetry.

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The topologically closest analogue with a well-established crystal structure I found is 3a-Hydroxy-trispiro(octahydropentalene-1,1':2,1'':3,1'''-tris(cyclopentane))-2'''-one ($\ce{C20H30O2}$). Its structure contains 3 vertex-sharing and one edge-sharing cyclopentane units (1):

enter image description here

Colorless product was obtained during photochemical 2+2 cyclodimerization of 2-cyclopentylidenecyclopentanone with several tertiary amines (triethylamine, N-methyldiisopropylamine and N-ethyldiisopropylamine) in acetonitrile solution upon irradiation with medium-pressure Hg-lamp.

(1) Ho, T.-I.; Peng, S.-M.; Lee, G.-H.; Lee, H.-C.; Hwang, T.-C. Acta Cryst C 1986, 42 (12), 1842–1844. DOI: 10.1107/S0108270186090339

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Scifinder, the online tool of the Chemical Abstracts Service of the American Chemical Society shows no results. Thus, unfortunately, to the best of any chemist’s knowledge this beautiful molecule has not yet been synthesised or isolated.

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