New family of tilings of three-dimensional Euclidean space by tetrahedra and octahedra.

Abstract:

:It is well known that two regular tetrahedra can be combined with a single regular octahedron to tile (complete fill) three-dimensional Euclidean space . This structure was called the "octet truss" by Buckminster Fuller. It was believed that such a tiling, which is the Delaunay tessellation of the face-centered cubic (fcc) lattice, and its closely related stacking variants, are the only tessellations of that involve two different regular polyhedra. Here we identify and analyze a unique family comprised of a noncountably infinite number of periodic tilings of whose smallest repeat tiling unit consists of one regular octahedron and six smaller regular tetrahedra. We first derive an extreme member of this unique tiling family by showing that the "holes" in the optimal lattice packing of octahedra, obtained by Minkowski over a century ago, are congruent tetrahedra. This tiling has 694 distinct concave (i.e., nonconvex) repeat units, 24 of which possess central symmetry, and hence is distinctly different and combinatorically richer than the fcc tetrahedra-octahedra tiling, which only has two distinct tiling units. Then we construct a one-parameter family of octahedron packings that continuously spans from the fcc to the optimal lattice packing of octahedra. We show that the "holes" in these packings, except for the two extreme cases, are tetrahedra of two sizes, leading to a family of periodic tilings with units composed four small tetrahedra and two large tetrahedra that contact an octahedron. These tilings generally possess 2,068 distinct concave tiling units, 62 of which are centrally symmetric.

authors

Conway JH,Jiao Y,Torquato S

doi

10.1073/pnas.1105594108

subject

Has Abstract

pub_date

2011-07-05 00:00:00

pages

11009-12

issue

27

eissn

0027-8424

issn

1091-6490

pii

1105594108

journal_volume

108

pub_type

杂志文章
  • Interactions of metal-nucleotide complexes with aspartate carbamoyltransferase in the crystalline state.

    abstract::We report the results of crystallographic difference maps at 3.0-A resolution of complexes of metal-nucleoside triphosphates with aspartate carbamoyltransferase (carbamoylphosphate:L-aspartate carbamoyltransferase, EC 2.1.3.2) from Escherichia coli. The complexes Gd3+-ATP, Al3+-ATP, and Gd3+-CTP bind to the allosteric...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.79.23.7171

    authors: Honzatko RB,Lipscomb WN

    更新日期:1982-12-01 00:00:00

  • Regulation of heme pathway enzymes and cellular glutathione content by metals that do not chelate with tetrapyrroles: blockade of metal effects by thiols.

    abstract::The trace metals nickel and platinum, which are not substrates for ferrochelatase and thus do not form heme in biological systems, were found to act similaryl to cobalt, and heme itself, in regulating heme metabolism in liver and kidney. These metals induced heme oxygenase activity in both organs with the peak of indu...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.74.5.1875

    authors: Maines MD,Kappas A

    更新日期:1977-05-01 00:00:00

  • Transmembrane E3 ligase RNF183 mediates ER stress-induced apoptosis by degrading Bcl-xL.

    abstract::The accumulation of misfolded proteins in the endoplasmic reticulum (ER) causes ER stress and triggers the unfolded protein response (UPR). Failure to resolve ER stress leads to apoptotic cell death via a yet unclear mechanism. Here, we show that RNF183, a membrane-spanning RING finger protein, localizes to the ER and...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1716439115

    authors: Wu Y,Li X,Jia J,Zhang Y,Li J,Zhu Z,Wang H,Tang J,Hu J

    更新日期:2018-03-20 00:00:00

  • Nanoparticle-mediated drug delivery to tumor vasculature suppresses metastasis.

    abstract::Integrin alphanubeta3 is found on a subset of tumor blood vessels where it is associated with angiogenesis and malignant tumor growth. We designed an alphanubeta3-targeted nanoparticle (NP) encapsulating the cytotoxic drug doxorubicin (Dox) for targeted drug delivery to the alphanubeta3-expressing tumor vasculature. W...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.0803728105

    authors: Murphy EA,Majeti BK,Barnes LA,Makale M,Weis SM,Lutu-Fuga K,Wrasidlo W,Cheresh DA

    更新日期:2008-07-08 00:00:00

  • Essential roles of the bHLH transcription factor Hrt2 in repression of atrial gene expression and maintenance of postnatal cardiac function.

    abstract::The basic helix-loop-helix transcriptional repressor Hairy-related transcription factor 2 (Hrt2) is expressed in ventricular, but not atrial, cardiomyocytes, and in endothelial and vascular smooth muscle cells. Mice homozygous for a null mutation of Hrt2 die perinatally from a spectrum of cardiac abnormalities, raisin...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.0702447104

    authors: Xin M,Small EM,van Rooij E,Qi X,Richardson JA,Srivastava D,Nakagawa O,Olson EN

    更新日期:2007-05-08 00:00:00

  • Oscillatory AAA+ ATPase Knk1 constitutes a novel morphogenetic pathway in fission yeast.

    abstract::Cellular morphogenesis relies partly on cell polarization by the cytoskeleton. In the fission yeast Schizosaccharomyces pombe, it is well established that microtubules (MTs) deliver the spatial cue Tea1, a kelch repeat protein, to the tip regions to direct the growth machinery at the cell tips driving the linear exten...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1407226111

    authors: Scheffler K,Recouvreux P,Paoletti A,Tran PT

    更新日期:2014-12-16 00:00:00

  • Stable integrative transformation of Trypanosoma brucei that occurs exclusively by homologous recombination.

    abstract::A calmodulin-neomycin-resistance fusion gene was introduced into Trypanosoma brucei by electroporation, and stably transformed cell lines were obtained. In all of the transformants, the fusion gene had integrated into the host genome at the cognate locus, evidently by homologous recombination within flanking calmoduli...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.88.6.2118

    authors: Eid J,Sollner-Webb B

    更新日期:1991-03-15 00:00:00

  • Accelerated tumor development in interferon-treated B6.C-Hyal-1 a mice.

    abstract::The Hyal-1 locus, which we have previously described and mapped to mouse chromosome 9, influences the serum levels and molecular weight forms of hyaluronidase. We have also shown that the growth of two transplantable tumors, the 3LL carcinoma and the B16F10 melanoma, is influenced by the alleles at Hyal-1, in that the...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.90.12.5708

    authors: De Maeyer-Guignard J,Lauret E,Eusèbe L,De Maeyer E

    更新日期:1993-06-15 00:00:00

  • Unsaturated nanoporomechanics.

    abstract::Although some important advances in the modeling of sorption and hygrothermal deformations of nanoporous materials such as hydrated cement paste, shale, coal, and some other rocks and soils have already been made, a comprehensive nanoporomechanics theory remains elusive. Here we strive to formulate it based on Gibb's ...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1919337117

    authors: Nguyen H,Rahimi-Aghdam S,Bažant ZP

    更新日期:2020-02-18 00:00:00

  • Protective effect of transforming growth factor beta 1 on experimental autoimmune diseases in mice.

    abstract::Interleukin 1 (IL-1) and tumor necrosis factor alpha are thought to contribute to the inflammatory response associated with autoimmune diseases. Transforming growth factor beta 1 (TGF-beta 1) counteracts many effects of these cytokines and has various immunosuppressive properties. In the present study, it is shown tha...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.88.7.2918

    authors: Kuruvilla AP,Shah R,Hochwald GM,Liggitt HD,Palladino MA,Thorbecke GJ

    更新日期:1991-04-01 00:00:00

  • Complete amino acid sequence of variable domains from two monoclonal human anti-gamma globulins of the Wa cross-idiotypic group: suggestion that the J segments are involved in the structural correlate of the idiotype.

    abstract::The complete amino acid sequences of the variable regions of two human IgM anti-gamma globulins are reported. The two proteins, Sie and Wol, share idiotypic determinants that are distinct from those shared by the two previously sequenced IgM anti-gamma globulins, Lay and Pom [Capra, J. D. & Kehoe, J. M. (1974) Proc. N...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.78.6.3799

    authors: Andrews DW,Capra JD

    更新日期:1981-06-01 00:00:00

  • Adiponectin is critical in determining susceptibility to depressive behaviors and has antidepressant-like activity.

    abstract::Depression is a debilitating mental illness and is often comorbid with metabolic disorders such as type 2 diabetes. Adiponectin is an adipocyte-derived hormone with antidiabetic and insulin-sensitizing properties. Here we show that adiponectin levels in plasma are reduced in a chronic social-defeat stress model of dep...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1202835109

    authors: Liu J,Guo M,Zhang D,Cheng SY,Liu M,Ding J,Scherer PE,Liu F,Lu XY

    更新日期:2012-07-24 00:00:00

  • Functional organization of sensory input to the olfactory bulb glomerulus analyzed by two-photon calcium imaging.

    abstract::Glomeruli in the olfactory bulb are anatomically discrete modules receiving input from idiotypic olfactory sensory neurons. To examine the functional organization of sensory inputs to individual glomeruli, we loaded olfactory sensory neurons with a Ca(2+) indicator and measured odorant-evoked presynaptic Ca(2+) signal...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.0400438101

    authors: Wachowiak M,Denk W,Friedrich RW

    更新日期:2004-06-15 00:00:00

  • Oligomerization of CD4 is required for stable binding to class II major histocompatibility complex proteins but not for interaction with human immunodeficiency virus gp120.

    abstract::Previous studies have failed to detect an interaction between monomeric soluble CD4 (sCD4) and class II major histocompatibility complex (MHC) proteins, suggesting that oligomerization of CD4 on the cell surface may be required to form a stable class II MHC binding site. To test this possibility, we transfected the F4...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.92.14.6444

    authors: Sakihama T,Smolyar A,Reinherz EL

    更新日期:1995-07-03 00:00:00

  • A new malaria vector in Africa: Predicting the expansion range of Anopheles stephensi and identifying the urban populations at risk.

    abstract::In 2012, an unusual outbreak of urban malaria was reported from Djibouti City in the Horn of Africa and increasingly severe outbreaks have been reported annually ever since. Subsequent investigations discovered the presence of an Asian mosquito species; Anopheles stephensi, a species known to thrive in urban environme...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.2003976117

    authors: Sinka ME,Pironon S,Massey NC,Longbottom J,Hemingway J,Moyes CL,Willis KJ

    更新日期:2020-10-06 00:00:00

  • Fluorescence microscopy for simultaneous observation of 3D orientation and movement and its application to quantum rod-tagged myosin V.

    abstract::Single molecule fluorescence polarization techniques have been used for three-dimensional (3D) orientation measurements to observe the dynamic properties of single molecules. However, only few techniques can simultaneously measure 3D orientation and position. Furthermore, these techniques often require complex equipme...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1118472109

    authors: Ohmachi M,Komori Y,Iwane AH,Fujii F,Jin T,Yanagida T

    更新日期:2012-04-03 00:00:00

  • Foxg1 localizes to mitochondria and coordinates cell differentiation and bioenergetics.

    abstract::Forkhead box g1 (Foxg1) is a nuclear-cytosolic transcription factor essential for the forebrain development and involved in neurodevelopmental and cancer pathologies. Despite the importance of this protein, little is known about the modalities by which it exerts such a large number of cellular functions. Here we show ...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1515190112

    authors: Pancrazi L,Di Benedetto G,Colombaioni L,Della Sala G,Testa G,Olimpico F,Reyes A,Zeviani M,Pozzan T,Costa M

    更新日期:2015-11-10 00:00:00

  • Synthetic peptide homologous to beta protein from Alzheimer disease forms amyloid-like fibrils in vitro.

    abstract::Progressive amyloid deposition in senile plaques and cortical blood vessels may play a central role in the pathogenesis of Alzheimer disease. We have used x-ray diffraction and electron microscopy to study the molecular organization and morphology of macromolecular assemblies formed by three synthetic peptides homolog...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.84.19.6953

    authors: Kirschner DA,Inouye H,Duffy LK,Sinclair A,Lind M,Selkoe DJ

    更新日期:1987-10-01 00:00:00

  • Chromosomal double-strand break repair in Ku80-deficient cells.

    abstract::The x-ray sensitive hamster cell line xrs-6 is deficient in DNA double-strand break (DSB) repair and exhibits impaired V(D)J recombination. The molecular defect in this line is in the 80-kDa subunit of the Ku autoantigen, a protein that binds to DNA ends and recruits the DNA-dependent protein kinase to DNA. Using an I...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.93.17.8929

    authors: Liang F,Romanienko PJ,Weaver DT,Jeggo PA,Jasin M

    更新日期:1996-08-20 00:00:00

  • A phylogenetic analysis of myosin heavy chain type II sequences corroborates that Acoela and Nemertodermatida are basal bilaterians.

    abstract::Bilateria are currently subdivided into three superclades: Deuterostomia, Ecdysozoa, and Lophotrochozoa. Within this new taxonomic frame, acoelomate Platyhelminthes, for a long time held to be basal bilaterians, are now considered spiralian lophotrochozoans. However, recent 18S rDNA [small subunit (SSU)] analyses have...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.172390199

    authors: Ruiz-Trillo I,Paps J,Loukota M,Ribera C,Jondelius U,Baguna J,Riutort M

    更新日期:2002-08-20 00:00:00

  • Merkel disc is a serotonergic synapse in the epidermis for transmitting tactile signals in mammals.

    abstract::The evolution of sensory systems has let mammals develop complicated tactile end organs to enable sophisticated sensory tasks, including social interaction, environmental exploration, and tactile discrimination. The Merkel disc, a main type of tactile end organ consisting of Merkel cells (MCs) and Aβ-afferent endings,...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1610176113

    authors: Chang W,Kanda H,Ikeda R,Ling J,DeBerry JJ,Gu JG

    更新日期:2016-09-13 00:00:00

  • Local auxin biosynthesis regulation by PLETHORA transcription factors controls phyllotaxis in Arabidopsis.

    abstract::Lateral organ distribution at the shoot apical meristem defines specific and robust phyllotaxis patterns that have intrigued biologists and mathematicians for centuries. In silico studies have revealed that this self-organizing process can be recapitulated by modeling the polar transport of the phytohormone auxin. Phy...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1213497110

    authors: Pinon V,Prasad K,Grigg SP,Sanchez-Perez GF,Scheres B

    更新日期:2013-01-15 00:00:00

  • Evidence for pro-beta-nerve growth factor, a biosynthetic precursor to beta-nerve growth factor.

    abstract::The biosynthesis of beta-nerve growth factor (betaNGF) was studied in mouse submaxillary glands incubated with L-[(35)S]cystine. betaNGF was isolated from tissue extracts by the addition of antiserum against betaNGF and the washed immunoprecipitates were analyzed by sodium dodecyl sulfate gel electrophoresis. With sho...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.74.9.3647

    authors: Berger EA,Shooter EM

    更新日期:1977-09-01 00:00:00

  • Transcription of the polyoma virus genome: synthesis and cleavage of giant late polyoma-specific RNA.

    abstract::The size of virus-specific RNA synthesized in cultured mouse kidney cells infected with polyoma virus was estimated by electrophoresis and sedimentation analysis of RNA extracts from whole cells. Newly synthesized "late" polyoma-specific RNA appears as "giant" molecules of heterogeneous size, up to several times large...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.68.9.2231

    authors: Acheson NH,Buetti E,Scherrer K,Weil R

    更新日期:1971-09-01 00:00:00

  • Ancient pigs reveal a near-complete genomic turnover following their introduction to Europe.

    abstract::Archaeological evidence indicates that pig domestication had begun by ∼10,500 y before the present (BP) in the Near East, and mitochondrial DNA (mtDNA) suggests that pigs arrived in Europe alongside farmers ∼8,500 y BP. A few thousand years after the introduction of Near Eastern pigs into Europe, however, their charac...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 历史文章,杂志文章

    doi:10.1073/pnas.1901169116

    authors: Frantz LAF,Haile J,Lin AT,Scheu A,Geörg C,Benecke N,Alexander M,Linderholm A,Mullin VE,Daly KG,Battista VM,Price M,Gron KJ,Alexandri P,Arbogast RM,Arbuckle B,Bӑlӑşescu A,Barnett R,Bartosiewicz L,Baryshnikov G,Bons

    更新日期:2019-08-27 00:00:00

  • An empirical basis for Mach bands.

    abstract::Mach bands, the illusory brightness maxima and minima perceived at the initiation and termination of luminance gradients, respectively, are generally considered a direct perceptual manifestation of lateral inhibitory interactions among retinal or other lower order visual neurons. Here we examine an alternative explana...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.96.9.5239

    authors: Lotto RB,Williams SM,Purves D

    更新日期:1999-04-27 00:00:00

  • Age-specific incidence of cancer: Phases, transitions, and biological implications.

    abstract::The observation that the age-specific incidence curve of many carcinomas is approximately linear on a double logarithmic plot has led to much speculation regarding the number and nature of the critical events involved in carcinogenesis. By a consideration of colorectal and pancreatic cancers in the Surveillance Epidem...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.0801151105

    authors: Meza R,Jeon J,Moolgavkar SH,Luebeck EG

    更新日期:2008-10-21 00:00:00

  • Expression of a complete soybean leghemoglobin gene in root nodules of transgenic Lotus corniculatus.

    abstract::The complete soybean leghemoglobin lbc(3) gene was transferred into the legume Lotus corniculatus using an Agrobacterium rhizogenes vector system. Organ-specific expression of the soybean gene was observed in root nodules formed on regenerated transgenic plants after infection with Rhizobium loti. The primary transcri...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.84.16.5754

    authors: Stougaard J,Petersen TE,Marcker KA

    更新日期:1987-08-01 00:00:00

  • High in vivo rates of methionine biosynthesis in transformed human and malignant rat cells auxotrophic for methionine.

    abstract::Unlike normal cells, malignant rat and two simian virus 40-transformed human cell lines can neither grow nor survive in B12-and folate-supplemented media in which methionine is replaced by homocysteine. Yet three lines of evidence indicate that the malignant and transformed cells synthesize large amounts of methionine...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.73.5.1523

    authors: Hoffman RM,Erbe RW

    更新日期:1976-05-01 00:00:00

  • Continuous evolutionary change in Plio-Pleistocene mammals of eastern Africa.

    abstract::Much debate has revolved around the question of whether the mode of evolutionary and ecological turnover in the fossil record of African mammals was continuous or pulsed, and the degree to which faunal turnover tracked changes in global climate. Here, we assembled and analyzed large specimen databases of the fossil re...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 历史文章,杂志文章

    doi:10.1073/pnas.1504538112

    authors: Bibi F,Kiessling W

    更新日期:2015-08-25 00:00:00