It is well known that a triangle can be divided by mid-point refinement into four sub-triangles with the same shape. Similarly, a tetrahedron can be parted into eight subtetrahedra, which are generally not uniform in ...It is well known that a triangle can be divided by mid-point refinement into four sub-triangles with the same shape. Similarly, a tetrahedron can be parted into eight subtetrahedra, which are generally not uniform in shape. This paper proves that there exist a set of tetrahedra, which is called isometrically subdivisible tetrahedra(IST) and can be divided into eight isometric subtetrahedra, including identical and reflection ones. And a new classification of tetrahedra is put forward, based on which all tetrahedra can be categorized into 26 classes according to both the number of maximum equal edges and topological relations. The IST belongs only to three of the classes. That result provides a new viewpoint of spatial structure and may be used to tile or subdivide space uniformly or isometrically.展开更多
We report the detailed physical properties of quaternary compound Ba2BiFeS5 with the key structural ingredient of isolated FeS4 tetrahedra.Magnetization and heat capacity measurements clearly indicate that Ba2BiFeS5 h...We report the detailed physical properties of quaternary compound Ba2BiFeS5 with the key structural ingredient of isolated FeS4 tetrahedra.Magnetization and heat capacity measurements clearly indicate that Ba2BiFeS5 has a paramagnetic to antiferromagnetic transition at about 30 K.The calculated magnetic entropy above ordering temperature is much smaller than theoretical value for high-spin Fe^3+ion with S=5/2,implying the possible short-range antiferromagnetic fluctuation in Ba2BiFeS5.展开更多
A general local C-m(m greater than or equal to 0) tetrahedral interpolation scheme by polynomials of degree 4m + 1 plus low order rational functions from the given data is proposed. The scheme can have either 4m + 1 o...A general local C-m(m greater than or equal to 0) tetrahedral interpolation scheme by polynomials of degree 4m + 1 plus low order rational functions from the given data is proposed. The scheme can have either 4m + 1 order algebraic precision if C-2m data at vertices and C-m data on faces are given or k + E[k/3] + 1 order algebraic precision if C-k (k less than or equal to 2m) data are given at vertices. The resulted interpolant and its partial derivatives of up to order m are polynomials on the boundaries of the tetrahedra.展开更多
Two special tetrahedra packing clusters were analytically calculated and discussed.Diamond and double-diamond,periodic superstructures emerge.Both structures exemplify an efficient,congruent tetrahedra space tiling st...Two special tetrahedra packing clusters were analytically calculated and discussed.Diamond and double-diamond,periodic superstructures emerge.Both structures exemplify an efficient,congruent tetrahedra space tiling strategy.The diamond superstructure exhibits a remarkable packing density of φ∼0.76 exceeding maximal density for the packing of equal spheres.The presented architectures display long range order with specific,repetitive structural motifs.Due to their simple tetrahedral symmetry,the investigated clusters have the potential to become interesting,unique sub-units both in construction technology and in self-assembled systems design.The modified structure of presented cluster can entirely tile three-dimensional Euclidean space R^(3) through periodic tessellations.Moreover,detailed analysis of the cluster enables definition of a new plesiohedron.展开更多
Compounds containing(pseudo-)tetrahedral main group(semi-)metal units are fundamentally important in three aspects.First,they provide new strategies for the stabilization of tetrahedral units,such as Pn_(4)(Pn=P,As)an...Compounds containing(pseudo-)tetrahedral main group(semi-)metal units are fundamentally important in three aspects.First,they provide new strategies for the stabilization of tetrahedral units,such as Pn_(4)(Pn=P,As)and their isoelectronic analogs,in the coordination sphere of d-/f-block metal atoms.Second,they serve as first-step models for the activation of tetrahedral molecules.Third,they are starting materials for subsequent transformations toward larger clusters or materials.Partial or full isoelectronic replacement of the pnictogen atoms in P4 or As_(4) results in a variety of(pseudo-)tetrahedral anions,Tt_(4)^(4−)(Tt=Si,Ge,Sn,Si/Ge),(Ge_(3)Pn)^(3−)(Pn=P,As;formed in situ),(Tt_(2)Pn_(2))^(2−)(Tt/Pn=Ge/P,Ge/As,Sn/Sb,Sn/Bi,Pb/Sb,Pb/Bi),or(TrBi_(3))^(2−)(Tr=Ga,In,Tl),and also cations,(P3Ch)+(Ch=S,Se,Te).The anions have proven to be excellent starting materials and building blocks for multinary clusters in the context of Zintl chemistry.Such compounds,which push forward the boundary of intriguing P4 chemistry,have never been thoroughly summarized before.In this minireview,we introduce all known intact(pseudo-)tetrahedral group 13–15 units,as well as the coordination compounds based on them,along with two new missing links,[Au(η^(2-)Tt_(2)Bi_(2))_(2)]^(3−)(Tt=Sn,Pb).展开更多
The Raman spectra of synthetic hydroxyapatite (HAP), natural silicate, sulfate bearing apatite (NAP) and ellestadite (ELLE) were compared. Raman characteristics of [SO 4],[SiO 4] tetrahedra in apatite structure were d...The Raman spectra of synthetic hydroxyapatite (HAP), natural silicate, sulfate bearing apatite (NAP) and ellestadite (ELLE) were compared. Raman characteristics of [SO 4],[SiO 4] tetrahedra in apatite structure were discussed. As [SiO 4] and [SO 4] enter the structure, their Raman intensity increases and that of [PO 4] decreases. The ν 1 peaks of [PO 4],[SiO 4],[SO 4] shift to lower wave number region as tetrahedra T P bong length and volume of unit cell increase.展开更多
物体的三维重建技术一直是计算机视觉领域研究的热点问题,提出一种利用Kinect传感器获取的深度图像实现多幅深度图像融合完成物体三维重建的方法。在图像空间中对深度图像进行三角化,然后在尺度空间中融合所有三角化的深度图像构建分层...物体的三维重建技术一直是计算机视觉领域研究的热点问题,提出一种利用Kinect传感器获取的深度图像实现多幅深度图像融合完成物体三维重建的方法。在图像空间中对深度图像进行三角化,然后在尺度空间中融合所有三角化的深度图像构建分层有向距离场(hierarchical signed distance field),对距离场中所有的体素应用整体Delaunay三角剖分算法产生一个涵盖所有体素的凸包,并利用Marching Tetrahedra算法构造等值面,完成物体表面重建。实验结果表明,该方法利用Kinect传感器采集的不同方向37幅分辨率为640×480的深度图像完成目标物体的三维重建,仅需要48s,并且得到非常精细的重建效果。展开更多
基金Supported by National Key Basic Research Program(2004CB318000)National Natural Science Foundation of China(60573154,61227802 and 61379082)
文摘It is well known that a triangle can be divided by mid-point refinement into four sub-triangles with the same shape. Similarly, a tetrahedron can be parted into eight subtetrahedra, which are generally not uniform in shape. This paper proves that there exist a set of tetrahedra, which is called isometrically subdivisible tetrahedra(IST) and can be divided into eight isometric subtetrahedra, including identical and reflection ones. And a new classification of tetrahedra is put forward, based on which all tetrahedra can be categorized into 26 classes according to both the number of maximum equal edges and topological relations. The IST belongs only to three of the classes. That result provides a new viewpoint of spatial structure and may be used to tile or subdivide space uniformly or isometrically.
基金Project supported by the National Key Research and Development Program of China(Grant No.2016YFA0300504)the National Natural Science Foundation of China(Grant Nos.11574394,11774423,and 11822412)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(RUC)(Grant Nos.15XNLQ07,18XNLG14,and 19XNLG17)
文摘We report the detailed physical properties of quaternary compound Ba2BiFeS5 with the key structural ingredient of isolated FeS4 tetrahedra.Magnetization and heat capacity measurements clearly indicate that Ba2BiFeS5 has a paramagnetic to antiferromagnetic transition at about 30 K.The calculated magnetic entropy above ordering temperature is much smaller than theoretical value for high-spin Fe^3+ion with S=5/2,implying the possible short-range antiferromagnetic fluctuation in Ba2BiFeS5.
基金Key Research and Development Program of Shandong Province,China (No. 2021ZLGX01)the National Natural Science Foundation of China (No. 52071190)the Shandong Provincial Natural Science Foundation,China (No. ZR2021YQ34)。
基金Supported partially by NSFC under Project 1967108, Croucher Foundation of Hong Kong and FRG ofHong Kong Baptist University.
文摘A general local C-m(m greater than or equal to 0) tetrahedral interpolation scheme by polynomials of degree 4m + 1 plus low order rational functions from the given data is proposed. The scheme can have either 4m + 1 order algebraic precision if C-2m data at vertices and C-m data on faces are given or k + E[k/3] + 1 order algebraic precision if C-k (k less than or equal to 2m) data are given at vertices. The resulted interpolant and its partial derivatives of up to order m are polynomials on the boundaries of the tetrahedra.
基金supported by the H2020-INFRAIA-2016-2017 project under research grant"EUSMI-European infrastructure for spectroscopy,scattering and imaging of soft matter",contract number GA731019,funded under H2020-EU.1.4.1.2.-RIA.
文摘Two special tetrahedra packing clusters were analytically calculated and discussed.Diamond and double-diamond,periodic superstructures emerge.Both structures exemplify an efficient,congruent tetrahedra space tiling strategy.The diamond superstructure exhibits a remarkable packing density of φ∼0.76 exceeding maximal density for the packing of equal spheres.The presented architectures display long range order with specific,repetitive structural motifs.Due to their simple tetrahedral symmetry,the investigated clusters have the potential to become interesting,unique sub-units both in construction technology and in self-assembled systems design.The modified structure of presented cluster can entirely tile three-dimensional Euclidean space R^(3) through periodic tessellations.Moreover,detailed analysis of the cluster enables definition of a new plesiohedron.
基金supported by the German Research foundation(Deutsche Forschungsgemeinschaft,DFG)F.P.gratefully acknowledges a research fellowship by the Alexander von Humboldt foundation.
文摘Compounds containing(pseudo-)tetrahedral main group(semi-)metal units are fundamentally important in three aspects.First,they provide new strategies for the stabilization of tetrahedral units,such as Pn_(4)(Pn=P,As)and their isoelectronic analogs,in the coordination sphere of d-/f-block metal atoms.Second,they serve as first-step models for the activation of tetrahedral molecules.Third,they are starting materials for subsequent transformations toward larger clusters or materials.Partial or full isoelectronic replacement of the pnictogen atoms in P4 or As_(4) results in a variety of(pseudo-)tetrahedral anions,Tt_(4)^(4−)(Tt=Si,Ge,Sn,Si/Ge),(Ge_(3)Pn)^(3−)(Pn=P,As;formed in situ),(Tt_(2)Pn_(2))^(2−)(Tt/Pn=Ge/P,Ge/As,Sn/Sb,Sn/Bi,Pb/Sb,Pb/Bi),or(TrBi_(3))^(2−)(Tr=Ga,In,Tl),and also cations,(P3Ch)+(Ch=S,Se,Te).The anions have proven to be excellent starting materials and building blocks for multinary clusters in the context of Zintl chemistry.Such compounds,which push forward the boundary of intriguing P4 chemistry,have never been thoroughly summarized before.In this minireview,we introduce all known intact(pseudo-)tetrahedral group 13–15 units,as well as the coordination compounds based on them,along with two new missing links,[Au(η^(2-)Tt_(2)Bi_(2))_(2)]^(3−)(Tt=Sn,Pb).
文摘The Raman spectra of synthetic hydroxyapatite (HAP), natural silicate, sulfate bearing apatite (NAP) and ellestadite (ELLE) were compared. Raman characteristics of [SO 4],[SiO 4] tetrahedra in apatite structure were discussed. As [SiO 4] and [SO 4] enter the structure, their Raman intensity increases and that of [PO 4] decreases. The ν 1 peaks of [PO 4],[SiO 4],[SO 4] shift to lower wave number region as tetrahedra T P bong length and volume of unit cell increase.
文摘物体的三维重建技术一直是计算机视觉领域研究的热点问题,提出一种利用Kinect传感器获取的深度图像实现多幅深度图像融合完成物体三维重建的方法。在图像空间中对深度图像进行三角化,然后在尺度空间中融合所有三角化的深度图像构建分层有向距离场(hierarchical signed distance field),对距离场中所有的体素应用整体Delaunay三角剖分算法产生一个涵盖所有体素的凸包,并利用Marching Tetrahedra算法构造等值面,完成物体表面重建。实验结果表明,该方法利用Kinect传感器采集的不同方向37幅分辨率为640×480的深度图像完成目标物体的三维重建,仅需要48s,并且得到非常精细的重建效果。
